Question

(1a) 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.

(1b) A drawer contains 19 white socks and 5 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.

(1c) According to the Cologuard test website, 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 4.7 % 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.

(1d) A box contains 12 white marbles and 5 black marbles. Suppose we randomly draw a marble from the box, replace it, and then randomly draw another marble from the box. (This means that we might observe the same marble twice). What is the probability that both the marbles are white? Write your answer as a decimal accurate to three decimal places.

Answer 1