1 (a) If 14 women compete in the marathon at the Olympics, in how many different...

1 (a) If 14 women compete in the marathon at the Olympics, in how many different ways can the gold, silver and bronze medals be awarded?

(b) If a three person committee is chosen at random from a group of 15 people, how many different committees are possible?

(c) In a new lottery game called "Minibucks", you select four numbers between 1 and 28. If you match all four numbers with the four numbers chosen by the lottery that day, you win the jackpot. (It doesn't matter whether the order that the lottery selected the numbers matches the order that you selected the numbers). What is the minimum number of different Minibucks tickets you would need to buy for one drawing in order to be 100% certain to win the jackpot for that drawing?

(d) In a new lottery game called "Minibucks version 2", you select four numbers between 1 and 25. If you match exactly three of your numbers with the four numbers chosen by the lottery that day, you win $5. What is the probability that you win this prize? Write your answer as a decimal accurate to four decimal places.

(e) A drawer contains 16 white socks and 6 black socks. Two different socks are selected from the drawer at random. What is the probability that both of the selected socks are white? Write your answer as a decimal accurate to three decimal places.

(f) According to https://www.cologuardtest.com/meet-cologuard/how-effective-is-cologuard (Links to an external site.) , if a person with colon cancer is given a Cologuard test, the probability that colon cancer is diagnosed by the test is 92%. If a person without colon cancer is given a Cologuard test, the probability that colon cancer is incorrectly diagnosed by the test is 13%. (This means that the probability of a false positive test result is 13%, and the test is said to have 87% specificity). Suppose that 2.5 % of the population actually has colon cancer. If a person is diagnosed as having colon cancer based on a Cologuard test, what is the probability that the person actually has colon cancer? Write your answer as a decimal accurate to three decimal places.

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Colby Messinger answered 1 year ago

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