Hypergeometric Distribution (Optional) Quiz

PDF page 266: There are five characteristics of a hypergeometric experiment:

PDF page 267: Problem A candy dish contains 100 jelly beans and 80 gumdrops. Fifty candies are picked at random. What is the probability that 35 of the 50 are gumdrops? The two groups are jelly beans and gumdrops. Since the probability question asks for the probability of picking gumdrops, the group of interest (first group) is gumdrops. The size of the group of interest (first group) is 80. The size of the second group is 100. The size of the sample is 50 (jelly beans or gumdrops). Let X = the number of gumdrops in the sample of 50. X takes on the values x = 0, 1, 2, . . . , 50. What is the probability statement written mathematically? Solution P(x = 35)

PDF page 267: Problem A candy dish contains 100 jelly beans and 80 gumdrops. Fifty candies are picked at random. What is the probability that 35 of the 50 are gumdrops? The two groups are jelly beans and gumdrops. Since the probability question asks for the probability of picking gumdrops, the group of interest (first group) is gumdrops. The size of the group of interest (first group) is 80. The size of the second group is 100. The size of the sample is 50 (jelly beans or gumdrops). Let X = the number of gumdrops in the sample of 50. X takes on the values x = 0, 1, 2, . . . , 50. What is the probability statement written mathematically? Solution P(x = 35)

PDF page 267: Problem A candy dish contains 100 jelly beans and 80 gumdrops. Fifty candies are picked at random. What is the probability that 35 of the 50 are gumdrops? The two groups are jelly beans and gumdrops. Since the probability question asks for the probability of picking gumdrops, the group of interest (first group) is gumdrops. The size of the group of interest (first group) is 80. The size of the second group is 100. The size of the sample is 50 (jelly beans or gumdrops). Let X = the number of gumdrops in the sample of 50. X takes on the values x = 0, 1, 2, . . . , 50. What is the probability statement written mathematically? Solution P(x = 35)

PDF page 267: Problem Suppose a shipment of 100 DVD players is known to have 10 defective players. An inspector randomly chooses 12 for inspection. He is interested in determining the probability that, among the 12 players, at most two are defective. The two groups are the 90 non-defective DVD players and the 10 defective DVD players. The group of interest (first group) is the defective group because the probability question asks for the probability of at most two defective DVD players. The size of the sample is 12 DVD players. They may be non-defective or defective. Let X = the number of defective DVD players in the sample of 12. X takes on the values 0, 1, 2, . . . , 10. X may not take on the values 11 or 12. The sample size is 12, but there are only 10 defective DVD players. Write the probability statement mathematically. Solution P(x ≤ 2)

PDF page 267: Problem Suppose a shipment of 100 DVD players is known to have 10 defective players. An inspector randomly chooses 12 for inspection. He is interested in determining the probability that, among the 12 players, at most two are defective. The two groups are the 90 non-defective DVD players and the 10 defective DVD players. The group of interest (first group) is the defective group because the probability question asks for the probability of at most two defective DVD players. The size of the sample is 12 DVD players. They may be non-defective or defective. Let X = the number of defective DVD players in the sample of 12. X takes on the values 0, 1, 2, . . . , 10. X may not take on the values 11 or 12. The sample size is 12, but there are only 10 defective DVD players. Write the probability statement mathematically. Solution P(x ≤ 2)

PDF page 268: e. Let X = the number of men on the committee. x = 0, 1, 2, . . . , 7.

PDF page 268: e. Let X = the number of men on the committee. x = 0, 1, 2, . . . , 7.

PDF page 268: interested in the number of men on your committee. If the members of the committee are randomly selected, what is the probability that your committee has more than four men? This is a hypergeometric problem because you are choosing your committee from two groups (men and women).

PDF page 269: X takes on the values 0, 1, 2, 3, 4, where r = 6, b = 5, and n = 4. X ~ H(6, 5, 4)

PDF page 269: Find P(x = 2). P(x = 2) = .4545 (calculator or computer)

PDF page 268: X ~ H(r, b, n) Read this as X is a random variable with a hypergeometric distribution. The parameters are r, b, and n: r = the size of the group of interest (first group), b = the size of the second group, n = the size of the chosen sample.