If m things are distributed among a men and b women. Then, the chance that the number of things received by men is odd, is

Step-by-step solution

A particular thing is received by a man with probability, p= a a+b and by a woman with probability, q= b a+b . Now, this experiment is repeated m times. Since, probability in each trial remains same for the men or women. Thus, we can apply binomial distribution. Since, men should get odd number of things, so the random variable x would have x=1,3,5, Required probability aligned & =P(X=1)+P(X=3)+P(X=5)+ & = ^m G₁ p q^ m-1 + ^m C₃ p^3 q^ m-3 + ^m C₅ p^5 q^ m-5 + aligned = [ (q+p)^m-(q-p)^m 2 ]= [ 1- ( b a+b - a a+b )