Let A and B be two events such that one of the two events must occur. Given that the chance of occurrence of A is 2 3 the chance of occurrence of B , then odds in favour of B is

Step-by-step solution

Let P(A) and P(B) be the probabilities of events A and B respectively. Since one of the two events must occur, P(A) + P(B) = 1 . Given P(A) = 2 3 P(B) , substituting this into the sum equation: 2 3 P(B) + P(B) = 1 5 3 P(B) = 1 P(B) = 3 5 . Then P(A) = 1 - 3 5 = 2 5 . The odds in favour of B are defined as the ratio of the probability of occurrence of B to the probability of non-occurrence of B , which is P(B) : P(B^ c ) . P(B^ c ) = 1 - P(B) = 1 - 3 5 = 2 5 . Odds in favour of B = 3 5 : 2 5 = 3 : 2 . Answer: 3: 2