Find the probability of obtaining exactly two threes on four rolls of a fair die.
A) 0.559
B) 0.243
C) 0.068
D) 0.116
E) 0.131

Question

Find the probability of obtaining exactly two threes on four rolls of a fair die. ​
A) 0.559
B) 0.243
C) 0.068
D) 0.116
E) 0.131

Quizplus · Accepted Answer

The probability of rolling a three on any given roll of a fair die is 1/6. The probability of not rolling a three on any given roll is 5/6.

To find the probability of rolling exactly two threes in four rolls, we need to use the binomial distribution formula:

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

In this case, n=4 (the number of rolls), k=2 (the number of threes we want to roll), p=1/6 (the probability of rolling a three), and (1-p)=5/6 (the probability of not rolling a three).

P(X=2) = (4 choose 2) * (1/6)^2 * (5/6)^2
P(X=2) = 6 * 1/36 * 25/36
P(X=2) = 0.11574...

Rounding to three decimal places, we get:

P(X=2) ≈ 0.116

Therefore, the best choice is D.

Find the Probability of Obtaining Exactly Two Threes on Four