SOLUTION: This is the question: 2 events, A and B, are defined on a sample space S such that P(A|B)= 0.6, P(At least of the events occurs)= 0.8, and P(Exactly one of the events occurs)= 0.6.

Question 470503: This is the question: 2 events, A and B, are defined on a sample space S such that P(A|B)= 0.6, P(At least of the events occurs)= 0.8, and P(Exactly one of the events occurs)= 0.6. Find P(A) and P(B).
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
P(A|B) = 0.6,
P(A U B) = 0.8, and
P(A) + P(B) = 0.6.
From P(A U B) = P(A) + P(B) - P(A and B), we get P(A and B) = 0.2.
==> P(A|B) = P(A and B)/P(B), or 0.6 = 0.2/P(B), or P(B) = 0.2/0.6 = 1/3.
Hence, ==> 0.8 = P(A) + 1/3 - 0.2 ==> P(A) = 2/3.
RELATED QUESTIONS
Find the following probabilities: (A) Events A and B are mutually exclusive events... (answered by stanbon)

Find the following probabilities: A)Events A and B are mutually exclusive events... (answered by stanbon)

Find the following probabilities: (A)Events A and B are mutually exclusive events... (answered by jrfrunner)

This is the question: For 2 events A and B defined on a sample space S,... (answered by stanbon,robertb)

Suppose you roll a die once and flip a coin twice. Events are defined as follows: A =... (answered by Fombitz)

Let A and B be events in a sample space S such that P(A) = 0.6, P(B) = 0.4, and P(A... (answered by jim_thompson5910)

Let A and B be two events in a sample space S such that P(A) = 0.6, P(B) = 0.4, and P(A... (answered by stanbon)

A and B are events defined on a sample space, with P(A) = 0.5 and P(A and B) = 0.2. Find... (answered by Edwin McCravy)

7. Which of the following is a characteristic of a binomial probability experiment? A.... (answered by stanbon)