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11 January, 08:26

Suppose A and B are mutually exclusive events, and that P (B) = 0.03 and P (A OR B) = 0.52. Find P (A)

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  1. 11 January, 08:42
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    P (A) = 0.49

    Step-by-step explanation:

    Given:

    A and B are mutually exclusive events.

    P (B) = 0.03

    P (A or B) = 0.52

    If two events A and B are mutually exclusive events, then there are no elements common in both the events. So, the probability of their intersection is 0.

    Now, as per probability addition theorem:

    P (A or B) = P (A) + P (B) + P (A and B)

    For mutually exclusive events, P (A and B) = 0. So,

    P (A or B) = P (A) + P (B) + 0

    P (A or B) = P (A) + P (B)

    Plug in the given values and solve for P (A). This gives,

    0.52 = P (A) + 0.03

    P (A) = 0.52 - 0.03

    P (A) = 0.49

    Therefore, the probability of occurrence of event A is P (A) = 0.49.
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