STAT 215 – Homework #3
Due Date: Wednesday , February 19th, Beginning of Class
Section 2.3 Problems
29, 30, 33, 34
Poker Hands. In a poker hand consisting of 5 cards, find the probability of holding:
(a) 2 aces and 3 jacks.
(b) A full house (2 cards of one face value and 3 cards of another face value – part a is an example of one specific full house).
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Poker Chips. There are 3 white poker chips, 5 blue poker chips, and 1 red poker chip in a bag. You randomly select 3 poker chips from the bag.
(a) Calculate the probability that there is one of each chip color.
(b) Calculate the probability that there are no blue chips.
(c) Calculate the probability that there is at least one blue chip.
Section 2.4 Problems
45, 47, 60
Olympic Drug Testing: Assume there is a diagnostic blood test to detect use of a performance enhancing drug. This test will be administered to all Olympic athletes prior to competition. The test is not perfect, but the following information is known:
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- Among drug users, 98% had a positive test (true positive).
- Among individuals not using the drug, 5% had a positive test (false positive).
- Assume that 1% of athletes actually use the drug (prevalence of drug use).
(a) What is the probability of a randomly chosen athlete getting a positive test result?
(b) Given that an athlete tests positive, what is the probability that he/she really is using the drug?
(c) BONUS (1pt): Assuming the prevalence is correct (1%), what percentage of false positives would be allowable in order for the probability in (b) to be 0.9?
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