Suppose a fair die is rolled 10 times. What is the probability that a 6 will occur 3 times in the 10 rolls? Round your answer to six decimal places.
A)Pr(3 6-es) = 0.310091
B)Pr(3 6-es) = 0.155045
C)Pr(3 6-es) = 0.387613
D)Pr(3 6-es) = 0.232568
E)Pr(3 6-es) = 0.193807

Question

Suppose a fair die is rolled 10 times. What is the probability that a 6 will occur 3 times in the 10 rolls? Round your answer to six decimal places. ​
A)Pr(3 6-es) = 0.310091
B)Pr(3 6-es) = 0.155045
C)Pr(3 6-es) = 0.387613
D)Pr(3 6-es) = 0.232568
E)Pr(3 6-es) = 0.193807

Quizplus · Accepted Answer

The probability of rolling a 6 on one roll is 1/6. So the probability of rolling a 6 three times in a row is (1/6)^3. However, there are 10 different ways that the 3 sixes could occur in the sequence of 10 rolls (for example, the first three rolls could be sixes, or the second through fourth rolls could be sixes, etc.). So we need to multiply (1/6)^3 by the number of ways to choose 3 rolls from 10, which is 10 choose 3 or 120. Therefore, the probability of rolling a 6 three times in 10 rolls is (1/6)^3 * 120 = 0.155045, rounded to six decimal places.

Suppose a Fair Die Is Rolled 10 Times