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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.

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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.

This problem has been solved

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