CGPET 2015 Solved Paper

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+ ...
=[

(q+p)m−(q−p)m

2

]
=[

1−( b a+b − a a+b )m

2

][∵p+q=1]
=

(a+b)m−(b−a)m

2(a+b)m