the probability of rolling a die and getting a 6 is of course 1/6 and the probability of not getting a 6 is 5/6. If you roll the same die 8 times, what is the probability that 6 will show up twice?

0.261

Step-by-step explanation:

We use the Bernoulli trial method to solve this. The form of the answer goes thus:

P = nCr * x^2 * y^6

Where n is the total number of trials which is 8, while r is the expected number of success, 2 in this case. x is the probability of success 1/6 while y is the probability of failure 5/6 in this case.

P = 8C2 * (1/6) ^2 * (5/6) ^6

P = 28 * 0.028 * 0.335 = 0.261