If P(A) = 0.7, what is P(A^c)?

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Multiple Choice

If P(A) = 0.7, what is P(A^c)?

Complement rule: the probability of not A, written as P(A^c), equals 1 minus the probability of A. This works because A and A^c are disjoint and together cover all possible outcomes, so their probabilities add to 1. If P(A) = 0.7, then P(A^c) = 1 − 0.7 = 0.3. So the probability that A does not occur is 0.3. The other options would correspond to different ideas: 0.7 is P(A); 1.0 would imply A has zero probability; 0.5 has no relation to the given P(A).

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