4.1 Hypergeometric Distribution

A candy dish contains 30 jelly beans and 20 gumdrops. Ten candies are picked at random. What is the probability that 5 of the 10 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 A in the formula) is gumdrops. The size of the group of interest (first group) is 30. The size of th…

A bag contains letter tiles. Forty-four of the tiles are vowels, and 56 are consonants. Seven tiles are picked at random. You want to know the probability that four of the seven tiles are vowels. What is the group of interest, the size of the group of interest, and the size of the sample?

TSA officers claim that they randomly select boarding passengers for additional search of carry-on luggage. During the past hour, of the 100 passengers passing through the security point, 5 were silver-haired grandmothers, of which 3 were chosen for additional screening among the 20 total chosen for “enhanced vetting.” Calculate the relevant probability and comment.

There are a total of 200 balls in a bag. This includes 25 red balls. 40 balls are selected randomly out of the bag. 8 of them are found to be red. Find the relevant probability.

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…

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?

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.

1. In words, define the random variable X.
2. List the values that X may take on.
3. How many pages do you expect to advertise footwear on them?
4. Calculate the standard devia…

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.

1. In words, define the random variable X.
2. List the values that X may take on.
3. Are you choosing the nine athletes with or without replacem…