An experiment can result in one of five equally likely simple events, E1, E2, , E5. Events A, B, and C are defined as follows. A: E1, E5 P(A) = 0.4 B: E2, E3, E4, E5 P(B) = 0.8 C: E1, E2 P(C) = 0.4 Refer to the following probabilities. P(A ∩ B) = 0.2 P(A|B) = 0.25 P(B|A) = 0.5 P(B ∪ C) = 1 P(B|C) = 0.5 P(C|B) = 0.25
An experiment can result in one of five equally likely simple events, E1, E2, , E5. Events A, B, and C are defined as follows. A: E1, E5 P(A) = 0.4 B: E2, E3, E4, E5 P(B) = 0.8 C: E1, E2 P(C) = 0.4 Refer to the following probabilities. P(A ∩ B) = 0.2 P(A|B) = 0.25 P(B|A) = 0.5 P(B ∪ C) = 1 P(B|C) = 0.5 P(C|B) = 0.25
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter11: Data Analysis And Probability
Section11.8: Probabilities Of Disjoint And Overlapping Events
Problem 2C
Related questions
Question
An experiment can result in one of five equally likely simple events ,
E1, E2, , E5.
Events A, B, and C are defined as follows.A: E1, E5 | P(A) | = | 0.4 |
|
|||
B: E2, E3, E4, E5 | P(B) | = | 0.8 |
|
|||
C: E1, E2 | P(C) | = | 0.4 |
Refer to the following probabilities.
P(A ∩ B) | = | 0.2 |
P(A|B) | = | 0.25 |
P(B|A) | = | 0.5 |
P(B ∪ C) | = | 1 |
P(B|C) | = | 0.5 |
P(C|B) | = | 0.25 |
Use the Addition and Multiplication Rules to find the following probabilities.
(a)
P(A ∪ B)
P(A ∪ B)
= + − = (b)
P(A ∩ B)
P(A ∩ B) = · P(B)
= (c)
P(B ∩ C)
P(B ∩ C) = · P(C)
= Do the results agree with those obtained by listing the simple events in each?
P(A ∪ B) = P({E1, E2, E3, E4, E5}) | = | 1 |
P(A ∩ B) = P({E5}) | = | 0.2 |
P(B ∩ C) = P({E2}) | = | 0.2 |
YesNo
An experiment can result in one or both of the events A and B, with the probabilities shown below. Use the probability table to answer this question.
A | AC | |
---|---|---|
B | 0.37 | 0.41 |
BC | 0.15 | 0.07 |
Refer to the following probabilities.
P(A) | = | 0.52 |
P(B) | = | 0.78 |
P(A ∩ B) | = | 0.37 |
P(A ∪ B) | = | 0.93 |
P(A|B) | = | 0.474 |
P(B|A) | = | 0.712 |
Are events A and B independent? Explain.
Since , A and B independent.
![An experiment can result in one of five equally likely simple events, E,1, E2,
Es. Events A, B, and C are defined as
follows.
A: E1, Es
P(A) = 0.4
B: E2, E3, E4, E5 P(B)
= 0.8
C: E1, E2
P(C) = 0.4
Refer to the following probabilities.
P(A N B) = 0.2
P(A|B) = 0.25
P(B|A) = 0.5
P(B U C) = 1
P(B|C) = 0.5
P(C|B) = 0.25
Use the Addition and Multiplication Rules to find the following probabilities.
(a) P(A U B)
P(A U B) = ---Select--
+ --Select---
---Select--
(b) P(A N B)
P(A N B) = |---Select--- v
P(B) =
(c) P(B N C)
P(B N C) = -Select---
P(C) =
Do the results agree with those obtained by listing the simple events in each?
P(A U B) = P({E1, E2, E3, E4. E5}) = 1
P(A N B) = P({E5}) = 0.2
P(B N C) = P({E,}) :
= 0.2
Yes
No](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff08ae38d-2677-4bdb-9cc2-6394d85259af%2Fff76af31-4792-4344-a48f-127af0c56a06%2F3r8gtye_processed.png&w=3840&q=75)
Transcribed Image Text:An experiment can result in one of five equally likely simple events, E,1, E2,
Es. Events A, B, and C are defined as
follows.
A: E1, Es
P(A) = 0.4
B: E2, E3, E4, E5 P(B)
= 0.8
C: E1, E2
P(C) = 0.4
Refer to the following probabilities.
P(A N B) = 0.2
P(A|B) = 0.25
P(B|A) = 0.5
P(B U C) = 1
P(B|C) = 0.5
P(C|B) = 0.25
Use the Addition and Multiplication Rules to find the following probabilities.
(a) P(A U B)
P(A U B) = ---Select--
+ --Select---
---Select--
(b) P(A N B)
P(A N B) = |---Select--- v
P(B) =
(c) P(B N C)
P(B N C) = -Select---
P(C) =
Do the results agree with those obtained by listing the simple events in each?
P(A U B) = P({E1, E2, E3, E4. E5}) = 1
P(A N B) = P({E5}) = 0.2
P(B N C) = P({E,}) :
= 0.2
Yes
No
![An experiment can result in one or both of the events A and B, with the probabilities shown below. Use the probability table
to answer this question.
A
AC
В
0.37
0.41
BC
0.15
0.07
Refer to the following probabilities.
P(A)
P(B)
= 0.52
= 0.78
P(A N B)
P(A U B)
P(A|B)
P(B|A)
= 0.37
= 0.93
0.474
= 0.712
Are events A and B independent? Explain.
Since ---Select-
A and B ---Select--- v independent.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff08ae38d-2677-4bdb-9cc2-6394d85259af%2Fff76af31-4792-4344-a48f-127af0c56a06%2Fhgttj4o_processed.png&w=3840&q=75)
Transcribed Image Text:An experiment can result in one or both of the events A and B, with the probabilities shown below. Use the probability table
to answer this question.
A
AC
В
0.37
0.41
BC
0.15
0.07
Refer to the following probabilities.
P(A)
P(B)
= 0.52
= 0.78
P(A N B)
P(A U B)
P(A|B)
P(B|A)
= 0.37
= 0.93
0.474
= 0.712
Are events A and B independent? Explain.
Since ---Select-
A and B ---Select--- v independent.
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