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A day full of math games & activities. Find one near you.
If P(A) = 0.50, P(B) = 0.40, then, and P(A ∪ B) = 0.88, then P(B|A) =
Solution:
Given: P(A) = 0.50, P(B) = 0.40 and P(A ∪ B) = 0.88
We know that the conditional probability is P(B|A) = P(A ⋂ B) / P(A)
We have P(A ∪ B) = P(A) + P(B) - P(A ⋂ B)
⇒ P(A ⋂ B) = P(A) + P(B) - P(A ∪ B)
⇒ P(A ⋂ B) = 0.50 + 0.40 - 0.88
⇒ P(A ⋂ B) = 0.90 - 0.88
⇒ P(A ⋂ B) = 0.02
Now, P(B|A) = P(A ⋂ B) / P(A) = 0.02 / 0.50 = 0.04
P(B|A) = 0.04
Therefore, the value of P(B|A) is 0.04
If P(A) = 0.50, P(B) = 0.40, then, and P(A ∪ B) = 0.88, then P(B|A) =
Summary:
If P(A) = 0.50, P(B) = 0.40, then, and P(A ∪ B) = 0.88, then P(B|A) is 0.04
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