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22 September, 18:17

Problem 1: Given the following probabilities P (Ac) = 0.45, P (B) = 0.34, and P (B|A) = 0.23. Find the following probabilities:

P (A)

P (A and B)

P (A or B)

P (A|B)

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Answers (1)
  1. 22 September, 20:37
    0
    P (A) = 0.55

    P (A and B) = P (A∩B) = 0.1265

    P (A or B) = P (A∪B) = 0.7635

    P (A|B) = 0.3721

    Step-by-step explanation:

    P (A') = 0.45

    P (A) = 1-0.45=0.55

    P (B∩A) = ?

    P (B|A) = 0.23

    P (B|A) = (P (A∩B)) / P (A)

    0.23 = (P (A∩B)) / 0.55

    P (A∩B) = 0.23*0.55=0.1265

    P (A∪B) = P (A) + P (B) - P (A∩B)

    =0.55+0.34-0.1265

    =0.7635

    P (A|B) = [P (A∩B) ]/P (B) = 0.1265/0.34 ≈0.3721
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