Odds in favour of an event A are 2 to 1 and odds in favour of `A cup B` are 3 to 1. Consistant with his information the smallest and largest values fo

Question

Odds in favour of an event A are 2 to 1 and odds in favour of A∪B are 3 to 1. Consistant with his information the smallest and largest values for the probability of event B are given by A. 1 6 ≤P(B)≤ 1 3 B. 1 3 ≤P(B)≤ 1 2 C. 1 12 ≤P(B)≤ 3 4 D. none of these Select the correct answer from above options

Answer 1

Correct Answer - C We have, P(A)= 2 3 ,P(A∪B)= 3 4 ∴P(A∪B)=P(A)+P(B)-P(A∩B) ⇒ 3 4 = 2 3 +P(B)-P(A∩B) ⇒P(A∩B)=P(B)- 1 12 Now, 0≤P(A∩B)≤P(A) ⇒0≤P(B)- 1 12 ≤P(A)⇒ 1 12 ≤P(B)≤ 3 4