Given P, left parenthesis, A, right parenthesis, equals, 0, point, 4P(A)=0.4, P, left parenthesis, B, right parenthesis, equals, 0, point, 2, 6P(B)=0.26 and P, left parenthesis, A, or , B, right parenthesis, equals, 0, point, 4, 3, 6P(A or B)=0.436, find the value of P, left parenthesis, A, and , B, right parenthesisP(A and B), rounding to the nearest thousandth, if necessary.
Question
Given P, left parenthesis, A, right parenthesis, equals, 0, point, 4P(A)=0.4, P, left parenthesis, B, right parenthesis, equals, 0, point, 2, 6P(B)=0.26 and P, left parenthesis, A, or , B, right parenthesis, equals, 0, point, 4, 3, 6P(A or B)=0.436, find the value of P, left parenthesis, A, and , B, right parenthesisP(A and B), rounding to the nearest thousandth, if necessary.
Solution
To find the value of P(A and B), we can use the formula for the probability of the union of two events:
P(A or B) = P(A) + P(B) - P(A and B)
We can rearrange this formula to solve for P(A and B):
P(A and B) = P(A) + P(B) - P(A or B)
Substituting the given values:
P(A and B) = 0.4 + 0.26 - 0.436
P(A and B) = 0.224
So, the value of P(A and B) is 0.224, or 0.224 when rounded to the nearest thousandth.
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