What is the probability that 6 rolls of a fair die will show four exactly 2 times?
A)0.0134
B)0.0067
C)0.41667
D)0.20094

Question

What is the probability that 6 rolls of a fair die will show four exactly 2 times? 
A)0.0134
B)0.0067
C)0.41667
D)0.20094

Quizplus · Accepted Answer

The probability can be calculated using the binomial probability formula, which is P(X = k) = (n choose k) * p^k * (1-p)^(n-k), where n is the number of trials, k is the number of successful trials, p is the probability of success on a single trial, and (n choose k) is the binomial coefficient. For this problem, n = 6 (rolls), k = 2 (desired number of twos), and p = 1/6 (probability of rolling a two). Thus, P(X = 2) = (6 choose 2) * (1/6)^2 * (5/6)^4 = 15 * (1/36) * (625/1296) = 0.20094.

What Is the Probability That 6 Rolls of a Fair