Question 1119956: Please help me solve this in simple way. Thank You.
Suppose that A and B are two events for which P(A)=0.25, P(B)=0.73, and P(B|A)=0.52 Find each of the following:
A. P(AandB)=
B. P(AorB)=
C. P(A|B)=
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
The formal definition of conditional probability is
P(A|B) = (P(A and B))/(P(B))
Then P(A and B) = (P(A|B))*P(B).
So in your example, P(A and B) = (0.52)(0.25) = 0.13.
That makes P(A or B) = (0.25+0.73)-0.13 = 0.85; and P(A|B) = P(A and B)/P(B) = 0.13/0.73 = (approximately) 0.178.
I personally find the formal definition of conditional probability confusing.
My way of thinking of P(B|A) is that the sample space is only "A", and I want to know what part of A is also B. That makes it easy (for me!) to see that P(A and B) is equal to P(B|A) times P(A).
A picture with a Venn diagram can also help visualize the probabilities, if you are thinking of A as the sample space. In your example, P(A) is 0.25, and P(B|A) is 0.52 of A, or 0.52*0.25 = 0.13
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