If a 6-sided die is rolled 5 times and rolling a 2 is considered to be a success, what are the chances of rolling exactly three successes?
A) 32.15%
B) 33.33%
C) 0.32%
D) none of these
E) 16.67%

Question

Quizplus · Accepted Answer

The probability of rolling exactly three 2s in five rolls of a 6-sided die 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. Here, n=5 (five rolls), k=3 (three successes), and p=1/6 (the probability of rolling a 2). Thus, P(X = 3) = (5 choose 3) * (1/6)^3 * (5/6)^2 = 10 * (1/216) * (25/36) ≈ 0.3215 or 32.15%.

If a 6-Sided Die Is Rolled 5 Times and Rolling