Answer:
92.74%.
Explanation:
This is a binomial probability problem where the probability of rolling a six on a single roll of a fair die is p = 1/6, and the number of trials is n = 12.
Let X be the number of sixes rolled in 12 rolls. We want to find the probability of X ≤ 4.
Using the binomial probability formula, we have:
P(X ≤ 4) = Σ P(X = k) for k = 0 to 4where P(X = k) = (n choose k) p^k (1-p)^(n-k)
Thus, the probability of rolling no more than 4 sixes is:
P(X ≤ 4) = Σ P(X = k) for k = 0 to 4
= P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)
= (12 choose 0) (1/6)^0 (5/6)^12 + (12 choose 1) (1/6)^1 (5/6)^11 + (12 choose 2) (1/6)^2 (5/6)^10 + (12 choose 3) (1/6)^3 (5/6)^9 + (12 choose 4) (1/6)^4 (5/6)^8
= 0.9274 (rounded to four decimal places)
Therefore, the probability of rolling no more than 4 sixes in 12 rolls of a die is approximately 0.9274 or 92.74%.