We are only concerned with rolling a 2. This means that the only outcomes are either we get a 2 or not. This is a binomial distribution. We would apply the binomial distribution formula which is expressed as
P(x) = nCx * p^x * q^(n - x)
where
n = number of trials
x = number of successes
p = probability of success
q = probability of failure
From the information given,
n = 15
x = 3(we want the positive result 3 times)
Recall, the total outcomes on the cube are 1, 2, 3, 4, 5, 6. Thus, we can get 2 only once from 6 outcomes. Thus,
p = 1/6
q = 1 - p = 1 - 1/6 = 5/6
Thus,
P(x = 3) = 15C3 * (1/6)^3 * (5/6)^(15 - 3)
P(x = 3) = 455 * 0.00463 * 0.1122
P(x = 3) = 0.2364
Converting to percentage, we have
0.2364 * 100 = 23.64
Thus, the probability of rolling a 2 exactly 3 times out of 15 rolls of a number cube is 23.6%