The mailing list of an agency that markets scubadiving trips

The mailing list of an agency that markets scuba-diving trips to the Florida Keys contains 75% males and 25% females. The agency calls 31 people chosen at random from its list.

(a) What is the probability that 11 of the 31 people are men?


(b) What is the probability that the first woman is reached on the 9th call?

Solution

Binomial Distribution

PMF of B.D is = f ( k ) = ( n k ) p^k * ( 1- p) ^ n-k
Where     
k = number of successes in trials        
n = is the number of independent trials        
p = probability of success on each trial

a)
P( X = 11 ) = ( 31 11 ) * ( 0.75^11) * ( 1 - 0.75 )^20
= 0
It is zero, we definitely have more men in the sample

b)
P(First Women is reached in 9th call) = (0.75)^8*(0.25)=0.02502