Question
The prior probabilities for events A1 and A2 are P(A1) = 0.20 and P(A2) = 0.40....
The prior probabilities for events A1 and A2 are P(A1) = 0.20 and P(A2) = 0.40. It is also known that P(A1 ∩ A2) = 0. Suppose P(B | A1) = 0.20 and P(B | A2) = 0.05. If needed, round your answers to three decimal digits.
| (a) | Are A1 and A2 mutually exclusive? | ||||
| - Select your answer -YesNoItem 1 | |||||
| Explain your answer. | |||||
| The input in the box below will not be graded, but may be reviewed and considered by your instructor. | |||||
| (b) | Compute P(A1 ∩ B) and P(A2 ∩ B). | ||||
|
|||||
| (c) | Compute P(B). | ||||
| P(B) = | |||||
| (d) | Apply Bayes’ theorem to compute P(A1 | B) and P(A2 | B). | ||||
|
Homework Answers
Answer #1
Not the answer you're looking for?
Similar Questions
Show work, thank you! Suppose that A1, A2 and B are events where A1 and A2...
Show work, thank you!
Suppose that A1, A2 and B are events where A1 and A2 are
mutually exclusive events and P(A1) = .5, P(A2) = .5, P(B│A1) = .9,
P(B│A2) = .2.
Find P(A2│B)
A. 0.90
B. 0.20
C. 0.50
D. 0.18
Let A1, A2, . . . , An be n independent events in a sample space...
Let A1, A2, . . . , An be n independent events in a sample space
Ω, with respective probability pi = P (Ai). Give a simple
expression for the probability P(A1 ∪A2 ∪...∪An) in terms of p1,
p2, ..., pn. Let us now apply your result in a practical setting: a
robot undergoes n independent tests, which are such that for each
test the probability of failure is p. What is the probability that
the robot fails at least...
consider the following statements concerning the probabilities of two events, A and B: P(A U B)=...
consider the following statements concerning the probabilities
of two events, A and B: P(A U B)= 0.85, P(A/B)= 0.54, P(B)= 0.5 .
Determine whether the events A and B are: (a) mutually exclusive,
(b) independent
suppose events A and B are such that p(A)=0.25,P(B) =0.3 and P(B|A)= 0.5 i) compute P(AnB)...
suppose events A and B are such that p(A)=0.25,P(B)
=0.3 and P(B|A)= 0.5
i) compute P(AnB) and P(AuB)
ii) Are events A and B independent?
iii) Are events A and B mutually exclusive?
b)if P(A)=0.6, P(B)= 0.15 and P(B|A')=0.25, find the following
probabilities
I)P(B|A), P(A|B),P(AuB)
Let P(A) = 0.40, P(B) = 0.35, and P(A ∩ B) = 0.13. a. Are A...
Let P(A) = 0.40, P(B) =
0.35, and P(A ∩ B) = 0.13.
a. Are A and B independent
events?
A. Yes because P(A | B) =
P(A).
B. Yes because P(A ∩ B) ≠ 0.
C. No because P(A | B) ≠
P(A).
D. No because P(A ∩ B) ≠ 0.
b. Are A and B mutually
exclusive events?
A. Yes because P(A | B) =
P(A).
B. Yes because P(A ∩ B) ≠ 0.
C. No because P(A...
Problem 16-09 (Algorithmic) The purchase patterns for two brands of toothpaste can be expressed as a...
Problem 16-09 (Algorithmic)
The purchase patterns for two brands of toothpaste can be
expressed as a Markov process with the following transition
probabilities:
To
From
Special B
MDA
Special B
0.95
0.05
MDA
0.25
0.75
Which brand appears to have the most loyal customers?
Explain.
The input in the box below will not be graded, but may be reviewed
and considered by your instructor.
What are the projected market shares for the two brands? If
required, round your answer...
Given the probabilities p(a)=.3 and p(b)=.2, what is the probability of the union P(a union b)...
Given the probabilities p(a)=.3 and p(b)=.2, what is the
probability of the union P(a union b) if a and b are mutually
exclusive? If a and b are independent? If b is a subset of a?
Explain your answer.
Problem 16-09 (Algorithmic) The purchase patterns for two brands of toothpaste can be expressed as a...
Problem 16-09 (Algorithmic)
The purchase patterns for two brands of toothpaste can be
expressed as a Markov process with the following transition
probabilities:
To
From
Special B
MDA
Special B
0.90
0.10
MDA
0.15
0.85
Which brand appears to have the most loyal customers?
Special B
Explain.
The input in the box below will not be graded, but may be reviewed
and considered by your instructor.
What are the projected market shares for the two brands? If
required, round your...
A fair coin is tossed two times, and the events A and B are defined as...
A fair coin is tossed two times, and the events A and B are
defined as shown below. Complete parts a through d.
A: {at most one tail is observed}
B: {The number of tails observed is even}
D. Find P(A), P(B), P(AUB), P( Upper A Superscript c Baseline
right parenthesis, and P(AnB) by summing the probabilities of
the appropriate sample points.
P(A)= ? (Type an integer or simplified fraction.)
Find P(B). P(B)=? (Type an integer or simplified
fraction.)
FindP(AuB)....
A fair coin is tossed two times, and the events A and B are defined as...
A fair coin is tossed two times, and the events A and B are
defined as shown below. Complete parts a through d.
D. Find P(A), P(B), P(AUB), P( Upper A Superscript c Baseline
right parenthesis, and P(AnB) by summing the probabilities of
the appropriate sample points.
P(A)= ? (Type an integer or simplified fraction.)
Find P(B).
P(B)=? (Type an integer or simplified fraction.)
FindP(AuB).
P(AuB)=? (Type an integer or simplified fraction.)
Find P(Ac)
P(Ac)=? (Type an integer or...
ADVERTISEMENT
Need Online Homework Help?
Get Answers For Free
Most questions answered within 1 hours.
ADVERTISEMENT
Active Questions
asked 22 minutes ago
asked 22 minutes ago
asked 43 minutes ago
asked 43 minutes ago
asked 1 hour ago
asked 1 hour ago
asked 1 hour ago
asked 1 hour ago
asked 1 hour ago
asked 1 hour ago
asked 1 hour ago
asked 2 hours ago