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 70% males and 30% females. The agency calls 28people chosen at random from its list.

(a) What is the probability that 20 of the 28 people are men? (Use the binomial probability formula. Round your answer to four decimal places.)


(b) What is the probability that the first woman is reached on the 4th call? (That is, the first 4 calls give MMMF. Round your answer to four decimal places.)

Solution

n = no of people = 28

Prob for male p =0.70

No of males = 19.6

There are two outcomes and independent.

X - no of males follow a Binomial distribution.

P(X=20) = 0.1627

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b) P(MMMF) = P(x=3) in first 3 and P(women in 4th)

= 0.70³(0.30) = 0.1029