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Let A and B be events with P left parenthesis A right parenthesis equals 0.30 and P left parenthesis B right parenthesis equals 0.40. If P left parenthesis A union B right parenthesis equals 0.44, then what is P left parenthesis A vertical line B right parenthesis? (Round answer to nearest two decimal places)

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Let A and B be events with P left parenthesis A right parenthesis equals 0.30 and P left parenthesis B right parenthesis equals 0.40. If P left parenthesis A union B right parenthesis equals 0.44, then what is P left parenthesis A vertical line B right parenthesis? (Round answer to nearest two decimal places)

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To find P(A | B), we use the formula:

P(A | B) = P(A ∩ B) / P(B)

We know that:

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

Then we can rearrange the formula to find P(A ∩ B):

P(A ∩ B) = P(A) + P(B) - P(A ∪ B)

P(A ∩ B) = 0.30 + 0.40 - 0.44

P(A ∩ B) = 0.26

Now we can calculate P(A | B):

P(A | B) = 0.26 / 0.40

P(A | B) ≈ 0.65

Therefore, P(A | B) is approximately 0.65 when rounded to two decimal places.

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