Conditional Probability

AP Statistics· difficulty 4/5

Using the same tree as before with P(A) = 0.6, P(B|A) = 0.7, P(B|A^c) = 0.2.

0.6 A 0.4 A^c B 0.7 B^c 0.3 B 0.2 B^c 0.8

What is P(B)?

  • A

    0.08

  • B

    0.50

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  • C

    0.90

  • D

    0.42

Explanation

P(B) = P(A)*P(B|A) + P(A^c)*P(B|A^c) = 0.6(0.7) + 0.4(0.2) = 0.42 + 0.08 = 0.50.

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