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