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').​

Answer 1

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