1. If A and B are events with P(A)=3/8, P(B) = 1/2 and P (AnB) = 1/4 find P(A’nB’).​

Question

1. If A and B are events with P(A)=3/8, P(B) = 1/2 and P (AnB) = 1/4 find P(A’nB’).​

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Ruby 3 weeks 2021-10-04T01:34:51+00:00 1 Answer 0 views 0

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    2021-10-04T01:36:21+00:00

    GIVEN :

    A & B are two events.

    • P(A) = ⅜

    • P(B) = ½

    • P(A ⋂ B) = ¼

    TO FIND :

    P(A’ ⋂ B’) = ?

    SOLUTION :

    We know that –

    ▪︎ P(A’ ⋂ B’) = 1 – P(A ⋃ B) _______eq.(1)

    We also know that

    ▪︎ P(A B) = P(A) + P(B) P(A B) _____eq.(2)

    • Now put the values –

    => P(A ⋃ B) = (⅜) + (½) – (¼)

    => P(A ⋃ B) = ⅜ + ¼

    => P(A ⋃ B) = (3 + 2)/8

    => P(A ⋃ B) = ⅝

    Put the value of P(A ⋃ B) in eq.(1) –

    => P(A’ ⋂ B’) = 1 – P(A ⋃ B)

    => P(A’ ⋂ B’) = 1 – (⅝)

    => P(A’ ⋂ B’) = (8 – 5)/8

    => P(A’ ⋂ B’) = ⅜

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