If P(A) = 0.3, what is P(A^c) (the complement)?

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Multiple Choice

If P(A) = 0.3, what is P(A^c) (the complement)?

Explanation:
The basic idea is that the complement fills in what’s not in the event, so together A and A^c make up the entire sample space and their probabilities add up to 1. Therefore P(A^c) = 1 − P(A) = 1 − 0.3 = 0.7. This respects that probabilities cannot exceed 1 and that the total probability across all outcomes is 1. If you consider the other options: 0.3 would make P(A^c) equal to P(A), which would not sum to 1 with P(A) = 0.3. 0.5 would imply P(A) = 0.5, which contradicts the given. 1.3 is impossible for a probability since totals can’t exceed 1.

The basic idea is that the complement fills in what’s not in the event, so together A and A^c make up the entire sample space and their probabilities add up to 1. Therefore P(A^c) = 1 − P(A) = 1 − 0.3 = 0.7. This respects that probabilities cannot exceed 1 and that the total probability across all outcomes is 1.

If you consider the other options: 0.3 would make P(A^c) equal to P(A), which would not sum to 1 with P(A) = 0.3. 0.5 would imply P(A) = 0.5, which contradicts the given. 1.3 is impossible for a probability since totals can’t exceed 1.

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