SOLUTION: If P(A) = 0.7, P(B) = 0.3, and P(B | A) = 0.4 find P(A and B).

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Question 1094988: If P(A) = 0.7, P(B) = 0.3, and P(B | A) = 0.4 find P(A and B).
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Given:
P(A) = 0.7
P(B) = 0.3
P(B|A) = 0.4

Let
x = P(A and B)

Use the conditional formula to say
P(B|A) = P(B and A)/P(A)
P(B|A) = P(A and B)/P(A)
0.4 = x/0.7

Solve for x
0.4 = x/0.7
0.7*0.4 = 0.7*(x/0.7)
0.28 = x
x = 0.28
P(A and B) = 0.28

Final Answer: 0.28