The probabilities of the events A and B .

Question

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Answer 1

Question

Chapter 4, Problem 129E

(a)

To determine

To find: The probabilities of the events A and B.

(a)

Expert Solution

Answer to Problem 129E

Solution: The probabilities are as follows:

P(A)=136P(B)=1536

Explanation of Solution

Given: A={2 on the first roll}, B={8 or more on the first roll}.

Explanation:

Calculation: The sample space can be shown as follows:

S={(1,1)(1,2)(1,3)(1,4)(1,5)(1,6)(2,1)(2,2)(2,3)(2,4)(2,5)(2,6)(3,1)(3,2)(3,3)(3,4)(3,5)(3,6)(4,1)(4,2)(4,3)(4,4)(4,5)(4,6)(5,1)(5,2)(5,3)(5,4)(5,5)(5,6)(6,1)(6,2)(6,3)(6,4)(6,5)(6,6)}

So, using the sample space, a table can be formed as follows:

Sum	Favorable Outcomes
2	1
3	2
4	3
5	4
6	5
7	6
8	5
9	4
10	3
11	2
12	1

Using the table, for event A, there is only one way of getting a sum of two on the first roll and there are total 36 outcomes possible. Therefore:

P(A)=Favorable outcomesTotal outcomes=136

For event B, there are 15 ways of getting a sum of 8 or more on the first roll and there are total 36 outcomes possible. Therefore:

P(B)=Favorable outcomesTotal outcomes=5+4+3+2+136=1536

Hence, the probability P(A) is 136 and the probability P(B) is 1536.

(b)

To determine

To find: The probabilities of events A and B.

(b)

Expert Solution

Answer to Problem 129E

Solution: The probabilities are as follows:

P(A)=136P(B)=1536

Explanation of Solution

Given: A={2 on the first roll}, B={8 or more on the second roll}.

Explanation:

Calculation: By using the table in part (a), for event A, there is only one way of getting a sum of two on the first roll and there are total 36 outcomes possible. Therefore:

P(A)=Favorable outcomesTotal outcomes=136

By using the table in part (a), for event B, there are 15 ways of getting a sum of 8 or more on the second roll and there are total 36 outcomes possible. Therefore:

P(B)=Favorable outcomesTotal outcomes=5+4+3+2+136=1536

Hence, the probability P(A) is 136 and the probability P(B) is 1536.

(c)

To determine

To find: The probabilities of events A and B.

(c)

Expert Solution

Answer to Problem 129E

Solution: The probabilities are as follows:

P(A)=1036P(B)=636

Explanation of Solution

Given: A={5 or less on second roll}, B={4 or less on the first roll}.

Explanation:

Calculation: By using the table in part (a), for event A, there are 10 ways of getting a sum of 5 or less on the second roll and there are total 36 outcomes. Therefore:

P(A)=Favorable outcomesTotal outcomes=4+3+2+136=1036

By using the table in part (a), for event B, there are 6 ways of getting a sum of 4 or less on the first roll and there are total 36 outcomes possible. Therefore:

P(B)=Favorable outcomesTotal outcomes=3+2+136=636

Hence, the probability P(A) is 1036 and the probability P(B) is 636.

(d)

To determine

To find: The probabilities of events A and B.

(d)

Expert Solution

Answer to Problem 129E

Solution: The probabilities are as follows:

P(A)=1036P(B)=636

Explanation of Solution

Given: A={5 or less on second roll}, B={4 or less on the second roll}.

Explanation:

Calculation: By using the table in part (a), for event A, there are 10 ways of getting a sum of 5 or less on the second roll and there are total 36 outcomes possible. Therefore:

P(A)=Favorable outcomesTotal outcomes=4+3+2+136=1036

By using the table in part (a), for event B, there are 6 ways of getting a sum of 4 or less on the second roll and there are total 36 outcomes possible. Therefore:

P(B)=Favorable outcomesTotal outcomes=3+2+136=636

Hence, the probability P(A) is 1036 and the probability P(B) is 636.

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Students have asked these similar questions

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We consider a 4-dimensional stock price model given (under P) by dẴ₁ = µ· Xt dt + йt · ΣdŴt where (W) is an n-dimensional Brownian motion, π = (0.02, 0.01, -0.02, 0.05), 0.2 0 0 0 0.3 0.4 0 0 Σ= -0.1 -4a За 0 0.2 0.4 -0.1 0.2) and a E R. We assume that ☑0 = (1, 1, 1, 1) and that the interest rate on the market is r = 0.02. (a) Give a condition on a that would make stock #3 be the one with largest volatility. (b) Find the diversification coefficient for this portfolio as a function of a. (c) Determine the maximum diversification coefficient d that you could reach by varying the value of a? 2

Answer 2

Question

Chapter 4, Problem 129E

(a)

To determine

To find: The probabilities of the events A and B.

(a)

Expert Solution

Answer to Problem 129E

Solution: The probabilities are as follows:

P(A)=136P(B)=1536

Explanation of Solution

Given: A={2 on the first roll}, B={8 or more on the first roll}.

Explanation:

Calculation: The sample space can be shown as follows:

S={(1,1)(1,2)(1,3)(1,4)(1,5)(1,6)(2,1)(2,2)(2,3)(2,4)(2,5)(2,6)(3,1)(3,2)(3,3)(3,4)(3,5)(3,6)(4,1)(4,2)(4,3)(4,4)(4,5)(4,6)(5,1)(5,2)(5,3)(5,4)(5,5)(5,6)(6,1)(6,2)(6,3)(6,4)(6,5)(6,6)}

So, using the sample space, a table can be formed as follows:

Sum	Favorable Outcomes
2	1
3	2
4	3
5	4
6	5
7	6
8	5
9	4
10	3
11	2
12	1

Using the table, for event A, there is only one way of getting a sum of two on the first roll and there are total 36 outcomes possible. Therefore:

P(A)=Favorable outcomesTotal outcomes=136

For event B, there are 15 ways of getting a sum of 8 or more on the first roll and there are total 36 outcomes possible. Therefore:

P(B)=Favorable outcomesTotal outcomes=5+4+3+2+136=1536

Hence, the probability P(A) is 136 and the probability P(B) is 1536.

(b)

To determine

To find: The probabilities of events A and B.

(b)

Expert Solution

Answer to Problem 129E

Solution: The probabilities are as follows:

P(A)=136P(B)=1536

Explanation of Solution

Given: A={2 on the first roll}, B={8 or more on the second roll}.

Explanation:

Calculation: By using the table in part (a), for event A, there is only one way of getting a sum of two on the first roll and there are total 36 outcomes possible. Therefore:

P(A)=Favorable outcomesTotal outcomes=136

By using the table in part (a), for event B, there are 15 ways of getting a sum of 8 or more on the second roll and there are total 36 outcomes possible. Therefore:

P(B)=Favorable outcomesTotal outcomes=5+4+3+2+136=1536

Hence, the probability P(A) is 136 and the probability P(B) is 1536.

(c)

To determine

To find: The probabilities of events A and B.

(c)

Expert Solution

Answer to Problem 129E

Solution: The probabilities are as follows:

P(A)=1036P(B)=636

Explanation of Solution

Given: A={5 or less on second roll}, B={4 or less on the first roll}.

Explanation:

Calculation: By using the table in part (a), for event A, there are 10 ways of getting a sum of 5 or less on the second roll and there are total 36 outcomes. Therefore:

P(A)=Favorable outcomesTotal outcomes=4+3+2+136=1036

By using the table in part (a), for event B, there are 6 ways of getting a sum of 4 or less on the first roll and there are total 36 outcomes possible. Therefore:

P(B)=Favorable outcomesTotal outcomes=3+2+136=636

Hence, the probability P(A) is 1036 and the probability P(B) is 636.

(d)

To determine

To find: The probabilities of events A and B.

(d)

Expert Solution

Answer to Problem 129E

Solution: The probabilities are as follows:

P(A)=1036P(B)=636

Explanation of Solution

Given: A={5 or less on second roll}, B={4 or less on the second roll}.

Explanation:

Calculation: By using the table in part (a), for event A, there are 10 ways of getting a sum of 5 or less on the second roll and there are total 36 outcomes possible. Therefore:

P(A)=Favorable outcomesTotal outcomes=4+3+2+136=1036

By using the table in part (a), for event B, there are 6 ways of getting a sum of 4 or less on the second roll and there are total 36 outcomes possible. Therefore:

P(B)=Favorable outcomesTotal outcomes=3+2+136=636

Hence, the probability P(A) is 1036 and the probability P(B) is 636.

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Answer 3

Question

Chapter 4, Problem 129E

(a)

To determine

To find: The probabilities of the events A and B.

(a)

Expert Solution

Answer to Problem 129E

Solution: The probabilities are as follows:

P(A)=136P(B)=1536

Explanation of Solution

Given: A={2 on the first roll}, B={8 or more on the first roll}.

Explanation:

Calculation: The sample space can be shown as follows:

S={(1,1)(1,2)(1,3)(1,4)(1,5)(1,6)(2,1)(2,2)(2,3)(2,4)(2,5)(2,6)(3,1)(3,2)(3,3)(3,4)(3,5)(3,6)(4,1)(4,2)(4,3)(4,4)(4,5)(4,6)(5,1)(5,2)(5,3)(5,4)(5,5)(5,6)(6,1)(6,2)(6,3)(6,4)(6,5)(6,6)}

So, using the sample space, a table can be formed as follows:

Sum	Favorable Outcomes
2	1
3	2
4	3
5	4
6	5
7	6
8	5
9	4
10	3
11	2
12	1

Using the table, for event A, there is only one way of getting a sum of two on the first roll and there are total 36 outcomes possible. Therefore:

P(A)=Favorable outcomesTotal outcomes=136

For event B, there are 15 ways of getting a sum of 8 or more on the first roll and there are total 36 outcomes possible. Therefore:

P(B)=Favorable outcomesTotal outcomes=5+4+3+2+136=1536

Hence, the probability P(A) is 136 and the probability P(B) is 1536.

(b)

To determine

To find: The probabilities of events A and B.

(b)

Expert Solution

Answer to Problem 129E

Solution: The probabilities are as follows:

P(A)=136P(B)=1536

Explanation of Solution

Given: A={2 on the first roll}, B={8 or more on the second roll}.

Explanation:

Calculation: By using the table in part (a), for event A, there is only one way of getting a sum of two on the first roll and there are total 36 outcomes possible. Therefore:

P(A)=Favorable outcomesTotal outcomes=136

By using the table in part (a), for event B, there are 15 ways of getting a sum of 8 or more on the second roll and there are total 36 outcomes possible. Therefore:

P(B)=Favorable outcomesTotal outcomes=5+4+3+2+136=1536

Hence, the probability P(A) is 136 and the probability P(B) is 1536.

(c)

To determine

To find: The probabilities of events A and B.

(c)

Expert Solution

Answer to Problem 129E

Solution: The probabilities are as follows:

P(A)=1036P(B)=636

Explanation of Solution

Given: A={5 or less on second roll}, B={4 or less on the first roll}.

Explanation:

Calculation: By using the table in part (a), for event A, there are 10 ways of getting a sum of 5 or less on the second roll and there are total 36 outcomes. Therefore:

P(A)=Favorable outcomesTotal outcomes=4+3+2+136=1036

By using the table in part (a), for event B, there are 6 ways of getting a sum of 4 or less on the first roll and there are total 36 outcomes possible. Therefore:

P(B)=Favorable outcomesTotal outcomes=3+2+136=636

Hence, the probability P(A) is 1036 and the probability P(B) is 636.

(d)

To determine

To find: The probabilities of events A and B.

(d)

Expert Solution

Answer to Problem 129E

Solution: The probabilities are as follows:

P(A)=1036P(B)=636

Explanation of Solution

Given: A={5 or less on second roll}, B={4 or less on the second roll}.

Explanation:

Calculation: By using the table in part (a), for event A, there are 10 ways of getting a sum of 5 or less on the second roll and there are total 36 outcomes possible. Therefore:

P(A)=Favorable outcomesTotal outcomes=4+3+2+136=1036

By using the table in part (a), for event B, there are 6 ways of getting a sum of 4 or less on the second roll and there are total 36 outcomes possible. Therefore:

P(B)=Favorable outcomesTotal outcomes=3+2+136=636

Hence, the probability P(A) is 1036 and the probability P(B) is 636.

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Answer 4

Question

Chapter 4, Problem 129E

(a)

To determine

To find: The probabilities of the events A and B.

(a)

Expert Solution

Answer to Problem 129E

Solution: The probabilities are as follows:

P(A)=136P(B)=1536

Explanation of Solution

Given: A={2 on the first roll}, B={8 or more on the first roll}.

Explanation:

Calculation: The sample space can be shown as follows:

S={(1,1)(1,2)(1,3)(1,4)(1,5)(1,6)(2,1)(2,2)(2,3)(2,4)(2,5)(2,6)(3,1)(3,2)(3,3)(3,4)(3,5)(3,6)(4,1)(4,2)(4,3)(4,4)(4,5)(4,6)(5,1)(5,2)(5,3)(5,4)(5,5)(5,6)(6,1)(6,2)(6,3)(6,4)(6,5)(6,6)}

So, using the sample space, a table can be formed as follows:

Sum	Favorable Outcomes
2	1
3	2
4	3
5	4
6	5
7	6
8	5
9	4
10	3
11	2
12	1

Using the table, for event A, there is only one way of getting a sum of two on the first roll and there are total 36 outcomes possible. Therefore:

P(A)=Favorable outcomesTotal outcomes=136

For event B, there are 15 ways of getting a sum of 8 or more on the first roll and there are total 36 outcomes possible. Therefore:

P(B)=Favorable outcomesTotal outcomes=5+4+3+2+136=1536

Hence, the probability P(A) is 136 and the probability P(B) is 1536.

(b)

To determine

To find: The probabilities of events A and B.

(b)

Expert Solution

Answer to Problem 129E

Solution: The probabilities are as follows:

P(A)=136P(B)=1536

Explanation of Solution

Given: A={2 on the first roll}, B={8 or more on the second roll}.

Explanation:

Calculation: By using the table in part (a), for event A, there is only one way of getting a sum of two on the first roll and there are total 36 outcomes possible. Therefore:

P(A)=Favorable outcomesTotal outcomes=136

By using the table in part (a), for event B, there are 15 ways of getting a sum of 8 or more on the second roll and there are total 36 outcomes possible. Therefore:

P(B)=Favorable outcomesTotal outcomes=5+4+3+2+136=1536

Hence, the probability P(A) is 136 and the probability P(B) is 1536.

(c)

To determine

To find: The probabilities of events A and B.

(c)

Expert Solution

Answer to Problem 129E

Solution: The probabilities are as follows:

P(A)=1036P(B)=636

Explanation of Solution

Given: A={5 or less on second roll}, B={4 or less on the first roll}.

Explanation:

Calculation: By using the table in part (a), for event A, there are 10 ways of getting a sum of 5 or less on the second roll and there are total 36 outcomes. Therefore:

P(A)=Favorable outcomesTotal outcomes=4+3+2+136=1036

By using the table in part (a), for event B, there are 6 ways of getting a sum of 4 or less on the first roll and there are total 36 outcomes possible. Therefore:

P(B)=Favorable outcomesTotal outcomes=3+2+136=636

Hence, the probability P(A) is 1036 and the probability P(B) is 636.

(d)

To determine

To find: The probabilities of events A and B.

(d)

Expert Solution

Answer to Problem 129E

Solution: The probabilities are as follows:

P(A)=1036P(B)=636

Explanation of Solution

Given: A={5 or less on second roll}, B={4 or less on the second roll}.

Explanation:

Calculation: By using the table in part (a), for event A, there are 10 ways of getting a sum of 5 or less on the second roll and there are total 36 outcomes possible. Therefore:

P(A)=Favorable outcomesTotal outcomes=4+3+2+136=1036

By using the table in part (a), for event B, there are 6 ways of getting a sum of 4 or less on the second roll and there are total 36 outcomes possible. Therefore:

P(B)=Favorable outcomesTotal outcomes=3+2+136=636

Hence, the probability P(A) is 1036 and the probability P(B) is 636.

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Answer 5

Chapter 4, Problem 129E

(a)

To determine

To find: The probabilities of the events A and B.

(a)

Expert Solution

Answer to Problem 129E

Solution: The probabilities are as follows:

P(A)=136P(B)=1536

Explanation of Solution

Given: A={2 on the first roll}, B={8 or more on the first roll}.

Explanation:

Calculation: The sample space can be shown as follows:

S={(1,1)(1,2)(1,3)(1,4)(1,5)(1,6)(2,1)(2,2)(2,3)(2,4)(2,5)(2,6)(3,1)(3,2)(3,3)(3,4)(3,5)(3,6)(4,1)(4,2)(4,3)(4,4)(4,5)(4,6)(5,1)(5,2)(5,3)(5,4)(5,5)(5,6)(6,1)(6,2)(6,3)(6,4)(6,5)(6,6)}

So, using the sample space, a table can be formed as follows:

Sum	Favorable Outcomes
2	1
3	2
4	3
5	4
6	5
7	6
8	5
9	4
10	3
11	2
12	1

Using the table, for event A, there is only one way of getting a sum of two on the first roll and there are total 36 outcomes possible. Therefore:

P(A)=Favorable outcomesTotal outcomes=136

For event B, there are 15 ways of getting a sum of 8 or more on the first roll and there are total 36 outcomes possible. Therefore:

P(B)=Favorable outcomesTotal outcomes=5+4+3+2+136=1536

Hence, the probability P(A) is 136 and the probability P(B) is 1536.

(b)

To determine

To find: The probabilities of events A and B.

(b)

Expert Solution

Answer to Problem 129E

Solution: The probabilities are as follows:

P(A)=136P(B)=1536

Explanation of Solution

Given: A={2 on the first roll}, B={8 or more on the second roll}.

Explanation:

Calculation: By using the table in part (a), for event A, there is only one way of getting a sum of two on the first roll and there are total 36 outcomes possible. Therefore:

P(A)=Favorable outcomesTotal outcomes=136

By using the table in part (a), for event B, there are 15 ways of getting a sum of 8 or more on the second roll and there are total 36 outcomes possible. Therefore:

P(B)=Favorable outcomesTotal outcomes=5+4+3+2+136=1536

Hence, the probability P(A) is 136 and the probability P(B) is 1536.

(c)

To determine

To find: The probabilities of events A and B.

(c)

Expert Solution

Answer to Problem 129E

Solution: The probabilities are as follows:

P(A)=1036P(B)=636

Explanation of Solution

Given: A={5 or less on second roll}, B={4 or less on the first roll}.

Explanation:

Calculation: By using the table in part (a), for event A, there are 10 ways of getting a sum of 5 or less on the second roll and there are total 36 outcomes. Therefore:

P(A)=Favorable outcomesTotal outcomes=4+3+2+136=1036

By using the table in part (a), for event B, there are 6 ways of getting a sum of 4 or less on the first roll and there are total 36 outcomes possible. Therefore:

P(B)=Favorable outcomesTotal outcomes=3+2+136=636

Hence, the probability P(A) is 1036 and the probability P(B) is 636.

(d)

To determine

To find: The probabilities of events A and B.

(d)

Expert Solution

Answer to Problem 129E

Solution: The probabilities are as follows:

P(A)=1036P(B)=636

Explanation of Solution

Given: A={5 or less on second roll}, B={4 or less on the second roll}.

Explanation:

Calculation: By using the table in part (a), for event A, there are 10 ways of getting a sum of 5 or less on the second roll and there are total 36 outcomes possible. Therefore:

P(A)=Favorable outcomesTotal outcomes=4+3+2+136=1036

By using the table in part (a), for event B, there are 6 ways of getting a sum of 4 or less on the second roll and there are total 36 outcomes possible. Therefore:

P(B)=Favorable outcomesTotal outcomes=3+2+136=636

Hence, the probability P(A) is 1036 and the probability P(B) is 636.

Answer 6

Chapter 4, Problem 129E

(a)

To determine

To find: The probabilities of the events A and B.

(a)

Expert Solution

Answer to Problem 129E

Solution: The probabilities are as follows:

P(A)=136P(B)=1536

Explanation of Solution

Given: A={2 on the first roll}, B={8 or more on the first roll}.

Explanation:

Calculation: The sample space can be shown as follows:

S={(1,1)(1,2)(1,3)(1,4)(1,5)(1,6)(2,1)(2,2)(2,3)(2,4)(2,5)(2,6)(3,1)(3,2)(3,3)(3,4)(3,5)(3,6)(4,1)(4,2)(4,3)(4,4)(4,5)(4,6)(5,1)(5,2)(5,3)(5,4)(5,5)(5,6)(6,1)(6,2)(6,3)(6,4)(6,5)(6,6)}

So, using the sample space, a table can be formed as follows:

Sum	Favorable Outcomes
2	1
3	2
4	3
5	4
6	5
7	6
8	5
9	4
10	3
11	2
12	1

Using the table, for event A, there is only one way of getting a sum of two on the first roll and there are total 36 outcomes possible. Therefore:

P(A)=Favorable outcomesTotal outcomes=136

For event B, there are 15 ways of getting a sum of 8 or more on the first roll and there are total 36 outcomes possible. Therefore:

P(B)=Favorable outcomesTotal outcomes=5+4+3+2+136=1536

Hence, the probability P(A) is 136 and the probability P(B) is 1536.

Answer 7

Chapter 4, Problem 129E

(a)

To determine

To find: The probabilities of the events A and B.

Answer 8

(a)

Expert Solution

Answer to Problem 129E

Solution: The probabilities are as follows:

P(A)=136P(B)=1536

Answer 9

(a)

Expert Solution

Answer 10

(a)

Expert Solution

Answer 11

Expert Solution

Answer 12

Explanation of Solution

Given: A={2 on the first roll}, B={8 or more on the first roll}.

Explanation:

Calculation: The sample space can be shown as follows:

S={(1,1)(1,2)(1,3)(1,4)(1,5)(1,6)(2,1)(2,2)(2,3)(2,4)(2,5)(2,6)(3,1)(3,2)(3,3)(3,4)(3,5)(3,6)(4,1)(4,2)(4,3)(4,4)(4,5)(4,6)(5,1)(5,2)(5,3)(5,4)(5,5)(5,6)(6,1)(6,2)(6,3)(6,4)(6,5)(6,6)}

So, using the sample space, a table can be formed as follows:

Sum	Favorable Outcomes
2	1
3	2
4	3
5	4
6	5
7	6
8	5
9	4
10	3
11	2
12	1

Using the table, for event A, there is only one way of getting a sum of two on the first roll and there are total 36 outcomes possible. Therefore:

P(A)=Favorable outcomesTotal outcomes=136

For event B, there are 15 ways of getting a sum of 8 or more on the first roll and there are total 36 outcomes possible. Therefore:

P(B)=Favorable outcomesTotal outcomes=5+4+3+2+136=1536

Hence, the probability P(A) is 136 and the probability P(B) is 1536.

Answer 13

(b)

To determine

To find: The probabilities of events A and B.

(b)

Expert Solution

Answer to Problem 129E

Solution: The probabilities are as follows:

P(A)=136P(B)=1536

Explanation of Solution

Given: A={2 on the first roll}, B={8 or more on the second roll}.

Explanation:

Calculation: By using the table in part (a), for event A, there is only one way of getting a sum of two on the first roll and there are total 36 outcomes possible. Therefore:

P(A)=Favorable outcomesTotal outcomes=136

By using the table in part (a), for event B, there are 15 ways of getting a sum of 8 or more on the second roll and there are total 36 outcomes possible. Therefore:

P(B)=Favorable outcomesTotal outcomes=5+4+3+2+136=1536

Hence, the probability P(A) is 136 and the probability P(B) is 1536.

Answer 14

(b)

To determine

To find: The probabilities of events A and B.

Answer 15

(b)

Expert Solution

Answer to Problem 129E

Solution: The probabilities are as follows:

P(A)=136P(B)=1536

Answer 16

(b)

Expert Solution

Answer 17

(b)

Expert Solution

Answer 18

Expert Solution

Answer 19

Explanation of Solution

Given: A={2 on the first roll}, B={8 or more on the second roll}.

Explanation:

Calculation: By using the table in part (a), for event A, there is only one way of getting a sum of two on the first roll and there are total 36 outcomes possible. Therefore:

P(A)=Favorable outcomesTotal outcomes=136

By using the table in part (a), for event B, there are 15 ways of getting a sum of 8 or more on the second roll and there are total 36 outcomes possible. Therefore:

P(B)=Favorable outcomesTotal outcomes=5+4+3+2+136=1536

Hence, the probability P(A) is 136 and the probability P(B) is 1536.

Answer 20

(c)

To determine

To find: The probabilities of events A and B.

(c)

Expert Solution

Answer to Problem 129E

Solution: The probabilities are as follows:

P(A)=1036P(B)=636

Explanation of Solution

Given: A={5 or less on second roll}, B={4 or less on the first roll}.

Explanation:

Calculation: By using the table in part (a), for event A, there are 10 ways of getting a sum of 5 or less on the second roll and there are total 36 outcomes. Therefore:

P(A)=Favorable outcomesTotal outcomes=4+3+2+136=1036

By using the table in part (a), for event B, there are 6 ways of getting a sum of 4 or less on the first roll and there are total 36 outcomes possible. Therefore:

P(B)=Favorable outcomesTotal outcomes=3+2+136=636

Hence, the probability P(A) is 1036 and the probability P(B) is 636.

Answer 21

(c)

To determine

To find: The probabilities of events A and B.

Answer 22

(c)

Expert Solution

Answer to Problem 129E

Solution: The probabilities are as follows:

P(A)=1036P(B)=636

Answer 23

(c)

Expert Solution

Answer 24

(c)

Expert Solution

Answer 25

Expert Solution

Answer 26

Explanation of Solution

Given: A={5 or less on second roll}, B={4 or less on the first roll}.

Explanation:

Calculation: By using the table in part (a), for event A, there are 10 ways of getting a sum of 5 or less on the second roll and there are total 36 outcomes. Therefore:

P(A)=Favorable outcomesTotal outcomes=4+3+2+136=1036

By using the table in part (a), for event B, there are 6 ways of getting a sum of 4 or less on the first roll and there are total 36 outcomes possible. Therefore:

P(B)=Favorable outcomesTotal outcomes=3+2+136=636

Hence, the probability P(A) is 1036 and the probability P(B) is 636.

Answer 27

(d)

To determine

To find: The probabilities of events A and B.

(d)

Expert Solution

Answer to Problem 129E

Solution: The probabilities are as follows:

P(A)=1036P(B)=636

Explanation of Solution

Given: A={5 or less on second roll}, B={4 or less on the second roll}.

Explanation:

Calculation: By using the table in part (a), for event A, there are 10 ways of getting a sum of 5 or less on the second roll and there are total 36 outcomes possible. Therefore:

P(A)=Favorable outcomesTotal outcomes=4+3+2+136=1036

By using the table in part (a), for event B, there are 6 ways of getting a sum of 4 or less on the second roll and there are total 36 outcomes possible. Therefore:

P(B)=Favorable outcomesTotal outcomes=3+2+136=636

Hence, the probability P(A) is 1036 and the probability P(B) is 636.

Answer 28

(d)

To determine

To find: The probabilities of events A and B.

Answer 29

(d)

Expert Solution

Answer to Problem 129E

Solution: The probabilities are as follows:

P(A)=1036P(B)=636

Answer 30

(d)

Expert Solution

Answer 31

(d)

Expert Solution

Answer 32

Expert Solution

Answer 33

Explanation of Solution

Given: A={5 or less on second roll}, B={4 or less on the second roll}.

Explanation:

Calculation: By using the table in part (a), for event A, there are 10 ways of getting a sum of 5 or less on the second roll and there are total 36 outcomes possible. Therefore:

P(A)=Favorable outcomesTotal outcomes=4+3+2+136=1036

By using the table in part (a), for event B, there are 6 ways of getting a sum of 4 or less on the second roll and there are total 36 outcomes possible. Therefore:

P(B)=Favorable outcomesTotal outcomes=3+2+136=636