A die is rolled 2 times, and success is rolling a number greater than 3. Let x = number of success. Construct the binomial distribution that describes this experiment, and find the mean of this distribution.

Question

Quizplus · Accepted Answer

The binomial distribution is given by:
P(X=k) = nCk * p^k * (1-p)^(n-k)
where n is the number of trials, p is the probability of success, and k is the number of successes.

In this case, n = 2, p = 1/3 (since the only way to have a success is to roll 4, 5, or 6), and k can be either 0, 1, or 2.

So, the binomial distribution is:
P(X=0) = (2C0) * (1/3)^0 * (2/3)^2 = 4/9
P(X=1) = (2C1) * (1/3)^1 * (2/3)^1 = 8/27
P(X=2) = (2C2) * (1/3)^2 * (2/3)^0 = 4/27

The mean of this distribution is:
μ = np = 2*(1/3) = 2/3

Therefore, the best choice is B, which gives the correct binomial distribution and mean.

A Die Is Rolled 2 Times, and Success Is Rolling