Sometimes probability statements are expressed in terms of odds. The odds in favor of an event A are the following ratio. P(A) P(not A) = P(A) P(A) For instance, if P(A) = 0.60, then P(A) = 0.40 and the odds in favor of A are 6 = 0.60 0.40 4 = 3 2' written as 3 to 2 or 3:2. (a) Show that if we are given the odds in favor of event A as n:m, the probability of event A is given by the following. P(A) = n n+m Hint: Solve the following equation for P(A). n = P(A) m 1 - P(A) n(1 - P(A)) = - n nP(A) = n = n = ([ * x )(P(A)) )P(A) 1) P(A) + 1 )P(A) + nP(A)