Question

If a fair die is rolled 4 times, what is the probability, to the nearest thousandth, of getting exactly 1 one?

Answer 1

The probability of getting exactly 1 one when rolling a fair die 4 times is approximately 0.250.

Step-by-step explanation:

When rolling a fair six-sided die, each outcome has an equal probability of 1/6. To calculate the probability of getting exactly 1 one in 4 rolls, we can use the binomial probability formula. The probability of success (rolling a one) is 1/6, and the probability of failure (not rolling a one) is 5/6.

The formula for binomial probability is P(X = k) = C(n, k) * p^k * q^(n-k), where:

- n is the number of trials,

- k is the number of successful outcomes,

- p is the probability of success on a single trial, and

- q is the probability of failure on a single trial.

In this case, n = 4, k = 1, p = 1/6, and q = 5/6. Plugging these values into the formula:

`\[ P(X = 1) = C(4, 1) * (1/6)^1 * (5/6)^3 \]\[ P(X = 1) = 4 * (1/6) * (5/6)^3 \]\[ P(X = 1) ≈ 0.250 \]`

Therefore, the probability of getting exactly 1 one in 4 rolls is approximately 0.250, rounded to the nearest thousandth.