A fair standard die is rolled until a six appears.If X is the number of rolls that are necessary.What is the probability that X ≤ 2?
A)12/36
B)11/36
C)7/36
D)6/36

Question

Quizplus · Accepted Answer

The probability of getting a six in one roll is 1/6, and the probability of not getting a six in one roll is 5/6. The probability of getting a six on the first roll is 1/6, and the probability of not getting a six on the first roll is 5/6. The probability of getting a six on the second roll, given that a six did not appear on the first roll, is also 1/6. Therefore, the probability of getting a six in two rolls or less is the sum of the probabilities of getting a six on the first roll and getting a six on the second roll given that a six did not appear on the first roll, which is: 1/6 + (5/6)(1/6) = 11/36.

A Fair Standard Die Is Rolled Until a Six Appears