If P(A) equals 0.25, what is P(A^c)?

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Multiple Choice

If P(A) equals 0.25, what is P(A^c)?

Explanation:
Think about the complement: A^c includes all outcomes where A does not occur, and together A and A^c cover the entire sample space. Their probabilities add up to 1, so P(A^c) = 1 − P(A). With P(A) = 0.25, we get P(A^c) = 0.75. This matches the idea that if there’s a 25% chance A happens, there’s a 75% chance it does not. The other numbers wouldn’t fit because 0.25 would mirror P(A), 1.25 is impossible for a probability, and 0.50 would correspond to P(A) being 0.50.

Think about the complement: A^c includes all outcomes where A does not occur, and together A and A^c cover the entire sample space. Their probabilities add up to 1, so P(A^c) = 1 − P(A). With P(A) = 0.25, we get P(A^c) = 0.75. This matches the idea that if there’s a 25% chance A happens, there’s a 75% chance it does not. The other numbers wouldn’t fit because 0.25 would mirror P(A), 1.25 is impossible for a probability, and 0.50 would correspond to P(A) being 0.50.

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