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Thread: Probability based question

  1. #1
    Aug 2018
    Around the place

    Exclamation Probability based question

    Consider two independent events, A and B, where the P(A) is 0.45 and the probability that A does not occur or B occurs is 0.70. Determine the probability that event B occurs.

    Any help is greatly appreciated
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  2. #2
    MHF Contributor
    Nov 2010

    Re: Probability based question

    Two independent events means that $P(A\text{ and }B) = P(A)P(B)$.

    $$P(\text{not }A\text{ or }B) = P(\text{not }A)+P(B) - P(\text{not }A\text{ and }B) = (1-P(A))+P(B) - (1-P(A))P(B)$$

    Plugging in the numbers you know:

    $$0.7 = (1-0.45)+P(B)-(1-0.45)P(B)$$

    $$0.15 = 0.45P(B)$$

    $$P(B) = \dfrac{1}{3}$$
    Thanks from Vinod and HallsofIvy
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