Question

Find P(A'/B'), given P(A) = 3/4, P(B) = 9/20 and P(A∩B) = 1/4?
1. 1/20
2. 1/9
3. 1/11
4. 1/12

Answer 1

Correct Answer - Option 3 : 1/11

Given

P(A) = 3/4

P(B) = 9/20

P(A ∩ B) = 1/4

Calculaton

P(A ∪ B) = P(A) + P(B) – P(A ∩ B)

⇒ 3/4 + 9/20 – 1/4

⇒ 19/20

P(A/B) = P(A^' ∩ B¹)/P(B^') = 1 – P(A ∪ B)^'/[1 – P(B)]

⇒ [1 – 19/20]/[1 – 9/20]

⇒ 1/11

⇒ Probability P(A/B) IS 1/11