A safety engineer claims that only 60% of all drivers use seat belts on short

trips. The probability that exactly 2 out of five drivers will be using his seat belts is closest
to?

To find the probability that exactly 2 out of five drivers will be using their seat belts, we can use the binomial probability formula.

The binomial probability formula is given by:
P(X = k) = C(n, k) * p^k * (1-p)^(n-k)

Where:
P(X = k) is the probability of getting exactly k successes (in this case, exactly 2 out of 5 drivers using seat belts).
C(n, k) is the number of ways to choose k successes from n trials, also known as the binomial coefficient.
p is the probability of success in a single trial (in this case, the probability that a driver uses a seat belt).
n is the total number of trials (in this case, the total number of drivers).

Substituting the values into the formula:
P(X = 2) = C(5, 2) * (0.6)^2 * (1-0.6)^(5-2)

Calculating the values:
C(5, 2) = 5! / (2!(5-2)!) = 10
(0.6)^2 = 0.36
(1-0.6)^(5-2) = 0.064

Plugging the values back into the formula:
P(X = 2) = 10 * 0.36 * 0.064

Calculating the final result:
P(X = 2) = 0.2304

Therefore, the probability that exactly 2 out of five drivers will be using their seat belts is approximately 0.2304.