3.57 Consider the experiment depicted by the Venn diagram, with the sample space S containing five sample points. The sample points are assigned the following probabilities: P(E₁)=20, P(E₂) = .30, P(E₁)=30, P(E₁).10, P(E₁).10 E₁ A E₂0 E₂ E30 Es B S a. Calculate P(A), P(B), and P(AB) b. Suppose we know that event A has occurred, so that the reduced sample space consists of the three sample points in A-namely, E₁, E₂, and E₁. Use the formula for conditional probability to adjust the probabilities of these three sample points for the knowledge that A has occurred [i.e., P(E, A)]. Verify that the conditional probabilities are in the same proportion to one another as the original sample point probabilities. NW c.Calculate the conditional probability P(B|A) in two ways: (1) Add the adjusted (conditional) probabilities of the sample points in the intersection An B, as these represent the event that B occurs given that A has occurred; (2) use the formula for conditional probability: P(BA) P(ANB) P(A)
3.57 Consider the experiment depicted by the Venn diagram, with the sample space S containing five sample points. The sample points are assigned the following probabilities: P(E₁)=20, P(E₂) = .30, P(E₁)=30, P(E₁).10, P(E₁).10 E₁ A E₂0 E₂ E30 Es B S a. Calculate P(A), P(B), and P(AB) b. Suppose we know that event A has occurred, so that the reduced sample space consists of the three sample points in A-namely, E₁, E₂, and E₁. Use the formula for conditional probability to adjust the probabilities of these three sample points for the knowledge that A has occurred [i.e., P(E, A)]. Verify that the conditional probabilities are in the same proportion to one another as the original sample point probabilities. NW c.Calculate the conditional probability P(B|A) in two ways: (1) Add the adjusted (conditional) probabilities of the sample points in the intersection An B, as these represent the event that B occurs given that A has occurred; (2) use the formula for conditional probability: P(BA) P(ANB) P(A)
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
![a. Calculate P(A), P(B), and P(AB)
b. Suppose we know that event A has occurred, so that
the reduced sample space consists of the three sample
points in A-namely, E₁, E₂, and E₁. Use the formula for
conditional probability to adjust the probabilities of
these three sample points for the knowledge that A has
occurred [i.e., P(E: A)]. Verify that the conditional
3.57 Consider the experiment depicted by the Venn diagram,
with the sample space S containing five sample points. The
sample points are assigned the following probabilities:
P(E₁).20, P(E₂) = .30, P(E3) = .30, P(E₁).10, P(E)= .10 probabilities are in the same proportion to one another
as the original sample point probabilities.
NW c.Calculate the conditional probability P(B|A) in
two ways: (1) Add the adjusted (conditional)
probabilities of the sample points in the intersection
An B, as these represent the event that B occurs given
that A has occurred; (2) use the formula for conditional
probability:
E₁ •
A
E₂0
E₂ E30
Es B
P(BA)
d. Are events A and B independent? Why and why not?
P(An B)
P(A)
Verify that the two methods yield the same result.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6d785545-ecc0-4bc3-8efc-4072fcf42cdd%2Fb58614ab-b0a5-4576-95c0-5b3dd9cd487b%2Fp0rkw2j_processed.png&w=3840&q=75)
Transcribed Image Text:a. Calculate P(A), P(B), and P(AB)
b. Suppose we know that event A has occurred, so that
the reduced sample space consists of the three sample
points in A-namely, E₁, E₂, and E₁. Use the formula for
conditional probability to adjust the probabilities of
these three sample points for the knowledge that A has
occurred [i.e., P(E: A)]. Verify that the conditional
3.57 Consider the experiment depicted by the Venn diagram,
with the sample space S containing five sample points. The
sample points are assigned the following probabilities:
P(E₁).20, P(E₂) = .30, P(E3) = .30, P(E₁).10, P(E)= .10 probabilities are in the same proportion to one another
as the original sample point probabilities.
NW c.Calculate the conditional probability P(B|A) in
two ways: (1) Add the adjusted (conditional)
probabilities of the sample points in the intersection
An B, as these represent the event that B occurs given
that A has occurred; (2) use the formula for conditional
probability:
E₁ •
A
E₂0
E₂ E30
Es B
P(BA)
d. Are events A and B independent? Why and why not?
P(An B)
P(A)
Verify that the two methods yield the same result.
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