4.5 Hypergeometric Distribution
Drawing without replacement from two groups so the odds shift each draw, and counting favorable combinations to find how many of the group of interest appear.
8 exercises
4.5 Exercise 1
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 grou…
4.5 Exercise 3
Suppose a shipment of 100 laptops is known to have ten defective laptops. An inspector randomly chooses 12 for inspection. He is interested in determining the probability that, among the 12 laptops, at most two are defective. The two groups are the 90 non-defective laptops and the 10 defective laptops. The group of interest (first group) is the defective group because the probability question asks…
4.5 Exercise 5
This is a hypergeometric problem because you are choosing your committee from two groups (men and women).
a. Are you choosing with or without replacement?
b. What is the group of interest?
c. How many are in the group of interest?
d. How many are in the other group?
e. Let X = _________ on the committee. What values does X take on?
f. The probability question is P(_______).
4.5 Exercise 8
Use the following information to answer the next five exercises: Suppose that a group of statistics students is divided into two groups: business majors and non-business majors. There are 16 business majors in the group and seven non-business majors in the group. A random sample of nine students is taken. We are interested in the number of business majors in the sample.
In words, define the random…
4.5 Exercise 10
Use the following information to answer the next five exercises: Suppose that a group of statistics students is divided into two groups: business majors and non-business majors. There are 16 business majors in the group and seven non-business majors in the group. A random sample of nine students is taken. We are interested in the number of business majors in the sample.
What values does X take on?
4.5 Exercise 12
Use the following information to answer the next five exercises: Suppose that a group of statistics students is divided into two groups: business majors and non-business majors. There are 16 business majors in the group and seven non-business majors in the group. A random sample of nine students is taken. We are interested in the number of business majors in the sample.
On average (μ), how many wo…
4.5 Exercise 14
In one of its Spring catalogs, L.L. Bean® advertised footwear on 29 of its 192 catalog pages. Suppose we randomly survey 20 pages. We are interested in the number of pages that advertise footwear. Each page may be picked at most once.
- In words, define the random variable X.
- List the values that X may take on.
- Give the distribution of X. X ~ _____(_____,_____)
- How many pages do you expect to adver…
4.5 Exercise 16
Suppose that nine Massachusetts athletes are scheduled to appear at a charity benefit. The nine are randomly chosen from eight volunteers from the Boston Celtics and four volunteers from the New England Patriots. We are interested in the number of Patriots picked.
- In words, define the random variable X.
- List the values that X may take on.
- Give the distribution of X. X ~ _____(_____,_____)
- Are you…
Adapted from Introductory Statistics 2e © 2023 Rice University. Licensed under CC BY 4.0. Source: Introductory Statistics 2e. Imported at revision 50ec917.