Using P(color) = 0.53, P(haircut) = 0.40, and P(both) = 0.17, what is P(color OR haircut)?

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Multiple Choice

Using P(color) = 0.53, P(haircut) = 0.40, and P(both) = 0.17, what is P(color OR haircut)?

Explanation:
When two events can both happen, the probability that at least one occurs uses the union rule: P(color OR haircut) = P(color) + P(haircut) − P(both). Here that’s 0.53 + 0.40 − 0.17 = 0.76. The subtraction removes the overlap where both events happen, which would have been counted twice if we just added. So the probability is 0.76, a valid probability between 0 and 1.

When two events can both happen, the probability that at least one occurs uses the union rule: P(color OR haircut) = P(color) + P(haircut) − P(both). Here that’s 0.53 + 0.40 − 0.17 = 0.76. The subtraction removes the overlap where both events happen, which would have been counted twice if we just added. So the probability is 0.76, a valid probability between 0 and 1.

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