A fair die is rolled 10 times.What is the probability that an even number (2,4,or 6)will occur between 2 and 4 times?
A)0.6123
B)0.1709
C)0.1611
D)0.3662
E)0.3223

Question

Quizplus · Accepted Answer

The probability of rolling an even number on a fair die is 3/6 or 1/2.

To find the probability that an even number occurs between 2 and 4 times out of 10 rolls, we need to use binomial probability.

Let X be the number of even numbers rolled out of 10 rolls. Then X follows a binomial distribution with n = 10 and p = 1/2.

We want to find P(2 ≤ X ≤ 4).

Using a binomial probability table or calculator, we can calculate:

P(X = 2) = 0.0439
P(X = 3) = 0.1172
P(X = 4) = 0.2051

Therefore, P(2 ≤ X ≤ 4) = P(X = 2) + P(X = 3) + P(X = 4) = 0.0439 + 0.1172 + 0.2051 = 0.3662.

Therefore, the answer is D.

A Fair Die Is Rolled 10 Times