Question

Sharkey rolls a fair six-sided die 4 times. What is the

probability of him rolling an EVEN number exactly 3
times?

Answer 1

Using the binomial probability formula, the probability of rolling an even number exactly 3 times out of 4 rolls is 0.25, or 25%.

Step-by-step explanation:

To calculate the probability of Sharkey rolling an even number exactly 3 times out of 4 rolls of a fair six-sided die, we use the binomial probability formula. An even number can be rolled on a six-sided die in 3 ways (2, 4, or 6), so the probability of rolling an even number (event E) is ½ on each roll. We are looking to find the probability of E happening exactly 3 times (k = 3) in n = 4 trials (rolls).

The binomial probability formula is: P(X = k) = C(n, k) * p^k * (1 - p)^(n - k), where C(n, k) is the number of combinations of n items taken k at a time, and p is the probability of success on a single trial.

For Sharkey's scenario:

1. n (total number of trials) = 4
2. k (number of successful trials) = 3
3. p (probability of success on a single trial) = 0.5 (since there are 3 even numbers out of 6 possible outcomes)
4. q (probability of failure on a single trial) = 1 - p = 0.5

Using these values, we calculate:

P(X = 3) = C(4, 3) * (0.5)^3 * (0.5)^(4 - 3) = 4 * (0.5)^3 * (0.5) = 4 * 0.125 * 0.5 = 0.25

Thus, the probability of Sharkey rolling an even number 3 times out of 4 rolls is 0.25, or 25%.