Choose the correct answer. You roll one die 8 times. What is the probability of rolling exactly six fours?

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7. Choose the correct answer. You roll one die 8 times. What is the probability of rolling exactly six fours? A. 4.17 × 10⁻⁴ B. 3.81 × 10⁻⁶ C. 5.95 × 10⁻⁷ D. 2.14 × 10⁻⁵

SnapAndSolve AI · Accepted Answer

To find the probability of rolling exactly six fours when rolling a die 8 times, we use the binomial probability formula:

P(X = k) = C(n, k) * (p^k) * ((1-p)^(n-k))

Where:

n = number of trials (8)
k = number of successful trials (6)
p = probability of success on a single trial (1/6)

Substituting the values:

P(X = 6) = C(8, 6) * (1/6)^6 * (5/6)^2

Calculating:

C(8, 6) = 28
(1/6)^6 = 1/7776
(5/6)^2 = 25/36

P(X = 6) = 28 * (1/7776) * (25/36)

P(X = 6) ≈ 3.81 × 10⁻⁶

The correct answer is B. 3.81 × 10⁻⁶.

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Choose the correct answer. You roll one die 8 times. What is the probability of rolling exactly six fours?

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