Several million lottery tickets are sold, and 60% of the tickets are held by women. Five winning tickets will be drawn at random. a) What is the probability that three or fewer of the winners will be women? b) What is the probability that three of the winners will be of one gender and two of the winners will be of the other gender?

A pet store has 12 puppies, including 4 poodles, 4 terriers, and 4 retrievers. If Rebecka and Aaron, in that order, each select one puppy at random without replacement, find the probability that Aaron selects a retriever, given that Rebecka selects a poodle. The probability is (Type an integer or a fraction.)

A financial services committe had 60 members, of which 9 were women. If 7 members are selected at random, find the probability that the group of 7 would be composed as the following. a.6 men and 1 women b.5 men and 2 women c. at least one women

A college surveys the 1258 alumni from 2019 and 2020. Of the 679 alumni from 2019, 127 went on to graduate school. Of the 579 alumni from 2020, 196 went on to graduate school. Find the probability that an alumnus selected at random from 2019 and 2020 is as described. a) a 2019 alumnus? b) a 2020 alumnus? c) a 2019 alumnus who did not attend graduate school?