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.
A)
B)
C)
D)
E)

Question

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. ​
A) ​ 
B) ​ 
C) ​ 
D) ​ 
E) ​

Quizplus · Accepted Answer

The binomial distribution for this experiment has n = 2 (two dice rolls) and p = 1/3 (the probability of rolling a number greater than 3). Let X be the number of successes, then we have:

P(X = 0) = (2 choose 0) * (1/3)^0 * (2/3)^2 = 4/9 
P(X = 1) = (2 choose 1) * (1/3)^1 * (2/3)^1 = 4/9 
P(X = 2) = (2 choose 2) * (1/3)^2 * (2/3)^0 = 1/9

The mean of a binomial distribution with parameters n and p is given by np. Therefore, the mean of this distribution is 2 * 1/3 = 2/3.

Choice B correctly gives the binomial probabilities and mean for this experiment.

A Die Is Rolled 2 Times, and Success Is Rolling