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Probability and Conditional Probability

SAT Math· difficulty 4/5

P(A)=0.6P(A) = 0.6, P(B)=0.5P(B) = 0.5, P(A and B)=0.3P(A \text{ and } B) = 0.3. Are AA and BB independent?

  • A

    No, P(A)≠P(B)P(A) \ne P(B).

  • B

    Yes, P(A and B)=P(A)⋅P(B)=0.30P(A \text{ and } B) = P(A) \cdot P(B) = 0.30.

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  • C

    No, P(A∣B)=0P(A | B) = 0.

  • D

    Cannot be determined.

Explanation

P(A)⋅P(B)=0.6×0.5=0.30=P(A and B)P(A) \cdot P(B) = 0.6 \times 0.5 = 0.30 = P(A \text{ and } B), so they are independent.

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