Hypergeometric Distribution

1. A marble bag contains ten "steelies" and 15 "cat's eyes". If Laurie reaches into the bag and withdraws five marbles, what is the probability that she will get: a) exactly one steelie? b) at least two steelies? c) no cat's eyes?

2. In a club with 20 members, five have positions of authority. If a random poll of ten of the club members is taken, what is the probability that at least two of those poled have positions of authority?

3. Nick organized a school fun-raising draw to raise money for the purchase of a rowing shell. There were 500 tickets sold at $5.00 each. Two hundred of the tickets were sold internally to members of the student body and the remainder was sold in the community at large. If three prizes were drawn, what is the probability that a) none of the prizes were won by students? b) all of the prizes were won by students?

4. At an office party names were drawn out of a hat to pick teams for charades. There were ten females and six males at the party. What is the probability that the first team drawn (four members to a team) were all female?

5. In a class of 12 students, four have advanced aptitudes in Mathematics. If a ministry official randomly tests three students, what is the probability that all three of the students tested are gifted in Mathematics? 6. A box contains 80 good and ten defective screws. If ten screws are used, what is the probability that none are defective? 7. A bag of jelly beans contains ten red, 12 yellow and six green. What is the probability that a selection of five jelly beans:

a) contains all red jelly beans? b) contains two red, two yellow and one green? c) has no red beans.