Question

Johnathan has a history test. There are a total of 6 essay prompts, but Jonathan only...

Johnathan has a history test. There are a total of 6 essay prompts, but Jonathan only studies two of the prompts the night before the test. On the test day, the professor rolls a standard die three times to select three random essay questions. What is the probability that:

a. one essay Jonathan studied for is randomly chosen?

b. both essays Jonathan studied for are randomly chosen?

Math   Statistics-And-Probability   
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Homework Answers

Answer #1

Total number of essays = 6

Number of essays Jonathan studied = 2

Number of essays Jonathan did not study = 6 - 2 = 4

Number of ways to select r items from n, nCr = n!/(r! x (n-r)!)

a) P(one essay Jonathan studied for is randomly chosen) = Number of ways to chose 1 essay from the 2 Jonathan studied x Number of ways to chose 2 essays from the 4 Jonathan did not study / Total number of ways to chose 3 essays from total 6

= 2C1 x 4C2 / 6C3

= 0.6

b) P(both essays Jonathan studied for are randomly chosen) = Number of ways to chose 2 essays from the 2 Jonathan studied x Number of ways to chose 1 essays from the 4 Jonathan did not study / Total number of ways to chose 3 essays from total 6

= 2C2 x 4C1 / 6C3

= 0.2

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