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If P(A) = 0.60, P(B) = 0.58, and P(A ∪ B) = 0.70, then P(A ∩ B) is:Group of answer choices0.58.0.48.0.60.0.70.

Question

If P(A) = 0.60, P(B) = 0.58, and P(A ∪ B) = 0.70, then P(A ∩ B) is:Group of answer choices0.58.0.48.0.60.0.70.

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Solution

The probability of both events A and B occurring (P(A ∩ B)) is given by the formula P(A ∩ B) = P(A) + P(B) - P(A ∪ B).

Substituting the given values into the formula, we get:

P(A ∩ B) = P(A) + P(B) - P(A ∪ B) = 0.60 + 0.58 - 0.70 = 0.48.

Therefore, P(A ∩ B) is 0.48.

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