Question

Binomial probability A company has 500 employees, and 60% of them have children. Suppose that we randomly select 4 of these employees. Which of the following would find the probability that exactly 3 of the 4 employees selected have children? Choose 1 answer:​

Answer 1

To find the probability that exactly 3 of the 4 randomly selected employees have children, use the binomial probability formula with n = 4, k = 3, and p = 0.60, by calculating the combination C(4, 3), and then multiplying it by 0.60^3 and (1 - 0.60)^1.

Step-by-step explanation:

The probability that exactly 3 of the 4 employees selected have children, given that 60% of the 500 employees have children, can be found using the binomial probability formula. The formula for calculating the probability of k successes (in this case, employees with children) out of n trials (selected employees) is given by:

P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)

Where:

• C(n, k) is the combination of n things taken k at a time
• p is the probability of a success on an individual trial
• X is the random variable representing the number of successes

In this scenario, n = 4, k = 3, and p = 0.60 (or 60%). Plugging these values into the binomial formula, we calculate the probability that exactly 3 of the 4 employees randomly selected have children.

The calculations would follow this process:

1. Calculate the combination of selecting 3 employees out of 4, which is C(4, 3).
2. Calculate the power of the success probability, which is 0.60^3.
3. Calculate the power of the failure probability, which is (1 - 0.60)^1.
4. Multiply these values together to get the final probability.