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,ldots∴ Required probability =P(X=1)+P(X=3)+P(X=5 ... =mC1pqm−1+mC3p3qm−3+mC5p5qm−5+ ... =[