MDM4UI
Geometric Distribution: Waiting Times
- Tabulate and graph the geometric distributions for X = 0, 1, 2, 3 in the following situations.
a) p = 0.5b) p = 0.2c) p = 0.7
- In the repeated rolling of a single die, what is the probability that you will roll a five or a six for the first time on the fourth roll?
- If you repeatedly cut a deck of cards, what is the probability that you will cut an ace in fewer than five cuts?
- What are the odds against your rolling doubles in fewer than four rolls of two dice? (First calculate the chances, then convert to odds.)
- What is the expected number of people you would have to sample to find someone with the same birthday as yours?
- If a recent poll indicated that the Hippopotamus party had 9% popular support, what would be the expected number of people that a television interviewer must survey to obtain the opinion of a Hippo supporter?
- If 2% of the transactions at a bank are applications for loans, what is the probability that the first loan request on a given day occurs with the tenth customer?
- It is estimated that on a daily basis 15% of the customers at a local supermarket use the express checkout. What is the probability that one of the first five customers on a given day uses the express checkout?
- If the probability of Michiko getting an A on her math tests is 0.6, what is the probability that a) she will get her first A on the second test?
b) she will get an A on one or more of her first three tests?
10. A production process produces components of which 3 percent are defective.
a) What is the expected number of components produced before a defective one is made?
b) What is the probability that the first defective component will occur within the first five
components off the line?
Answers: 2. 8/813. 0.2744. 125:915. 3646. 107. 0.017
8. 0.5569. a) 0.24b) 0.93610. a) 32b) 0.141