Let A and B be events in a sample space S such that P(A) = 0.6, P(B) = 0.4, and P(A B) = 0.27. Find the probability
P(B|A)
by definition of conditional probability :
P(B|A) = P(B and A)/P(A)
= .27/.6 = .45
What is Baye's Theorem? http://en.wikipedia.org/wiki/Bayes%27_theorem
To find the probability P(B|A), which is the conditional probability of event B given event A, we need to use the formula:
P(B|A) = P(A B) / P(A)
Given information:
P(A) = 0.6
P(B) = 0.4
P(A B) = 0.27
Now, substitute these values into the formula:
P(B|A) = 0.27 / 0.6
Simplify the numerator and denominator:
P(B|A) = 0.45
Therefore, the probability of event B given event A (P(B|A)) is 0.45.