1) Let P(A) = 0.2, P(B) = 0.6 and P(A or B) =0.5. Are events A and B mutually exclusive? Why or why %3D not?

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(Round all answers to three decimal places.)
1) Let P(A) = 0.2, P(B) = 0.6 and P(A or B) =0.5. Are events A and B mutually exclusive? Why or why
not?
2) Suppose A and B are events such that P(A) = 0.6, P(B) = 0.7 and P(A or B) = 0.8.
Calculate the following:
a) P(A and B) =
b) P(A | B) =
c) P(B |A) =
d) P(A) =
e) P(B) =.
f) Are A and B mutually exclusive? Why or why not?
g) Are A and B independent? Why or why not?
3) One card is selected from an ordinary deck of 52 cards. Find the conditional probabilities:
(You can write answer as a fraction or decimal rounded to three decimal places.)
a) A spade given the card is black
b) A spade given the card is red_
c) A 4 given the card is not a picture card
d) A king given the card is a picture card
- A 1. - -t.. al
Transcribed Image Text:(Round all answers to three decimal places.) 1) Let P(A) = 0.2, P(B) = 0.6 and P(A or B) =0.5. Are events A and B mutually exclusive? Why or why not? 2) Suppose A and B are events such that P(A) = 0.6, P(B) = 0.7 and P(A or B) = 0.8. Calculate the following: a) P(A and B) = b) P(A | B) = c) P(B |A) = d) P(A) = e) P(B) =. f) Are A and B mutually exclusive? Why or why not? g) Are A and B independent? Why or why not? 3) One card is selected from an ordinary deck of 52 cards. Find the conditional probabilities: (You can write answer as a fraction or decimal rounded to three decimal places.) a) A spade given the card is black b) A spade given the card is red_ c) A 4 given the card is not a picture card d) A king given the card is a picture card - A 1. - -t.. al
4) An urn contains 8 balls: 4 orange, 3 red, and 1 green. Two balls are selected without replacement.
Find:
a) P(both balls are orange) =
b) P(both balls are green) =
c) P(both balls are red) =
d) P(the first ball is orange and the second is green) =
e) P(the first ball is red and the second is orange) =.
f) P(one is orange and one is green in any order) =
5) Let X represent the number of occupants in a randomly chosen car on a certain stretch of highway
during morning commute hours. A survey of cars showed that the probability distribution of X is as
follows.
1
4
5
P(x)
0.70
0.15
0.10
0.03
0.02
a) Find P(2).
b) Find P(More than 3).
c) Find the probability that a car has only one occupant.
d) Find the probability that a car has fewer than four occupants.
e) Compute the mean ux.
f) Compute the standard deviation ox.
6) An investor is considering a $30,000 investment in a start-up company. She estimates that she has
a probability of 0.30 of a $20,000 loss, probability of 0.20 of a $35,000 profit, probability of 0.35 of a
$45,000 profit, and probability 0.15 of breaking even (a profit of $0). Create a discrete probability
distribution. What is the expected value of the profit? Would you advise the investor to make the
investment? Explain why?
Transcribed Image Text:4) An urn contains 8 balls: 4 orange, 3 red, and 1 green. Two balls are selected without replacement. Find: a) P(both balls are orange) = b) P(both balls are green) = c) P(both balls are red) = d) P(the first ball is orange and the second is green) = e) P(the first ball is red and the second is orange) =. f) P(one is orange and one is green in any order) = 5) Let X represent the number of occupants in a randomly chosen car on a certain stretch of highway during morning commute hours. A survey of cars showed that the probability distribution of X is as follows. 1 4 5 P(x) 0.70 0.15 0.10 0.03 0.02 a) Find P(2). b) Find P(More than 3). c) Find the probability that a car has only one occupant. d) Find the probability that a car has fewer than four occupants. e) Compute the mean ux. f) Compute the standard deviation ox. 6) An investor is considering a $30,000 investment in a start-up company. She estimates that she has a probability of 0.30 of a $20,000 loss, probability of 0.20 of a $35,000 profit, probability of 0.35 of a $45,000 profit, and probability 0.15 of breaking even (a profit of $0). Create a discrete probability distribution. What is the expected value of the profit? Would you advise the investor to make the investment? Explain why?
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