Three hundred people apply for three jobs. 100 of the applicants are women.

Question

(a) If three persons are selected at random, what is the probability that all are women? (Round the answer to six decimal places.)

(b) If three persons are selected at random, what is the probability that two are women? (Round the answer to six decimal places.)

(c) If three persons are selected at random, what is the probability that one is a woman? (Round the answer to six decimal places.)

(d) If three persons are selected at random, what is the probability that none is a woman? (Round the answer to six decimal places.)

Answer 1

300 people apply for 3 jobs

100 are women applicants

a) if selected randomly what is the probability all 3 are women?

p(3W)= (100/300)(99/299)(98/298) = (1/3)(99/299)(49/149)=(33/299)(49/149)=.03629548158= 3.629548%

b) what is probability that exactly 2 are women?

p(2W) = 3C2(100/300)(99/299)(200/298) = .2222172342 = 22.221723%

c) what is the probability that 1 is a woman

p(1W) =3C1(100/300)(200/299)(199/298)=.4466790869= 44.667909%

d) what is the probability that 0 are women

p(0W) = (200/300)(199/299)(198/298) =.2948081973 = 29.480820%

if they sum to 100% that's correct. about 3.6+22.2+44.7+29.5= 100