Final answer:
The probability that a couple with four kids will have three boys and one girl is calculated using the binomial distribution formula. Given the probability of having a boy or girl is equal (0.5), the correct answer is 4/16.
Step-by-step explanation:
The question is about using the binomial probability formula to calculate the probability that a couple planning to have four children will have three boys and one girl, under the assumption that all outcomes have an equal chance (which is a simplification, as in real life other factors can influence gender probability). The binomial distribution model is appropriate since we have a fixed number of trials (four children), two possible outcomes (boy or girl), and a constant probability of each outcome on each trial.
The probability of having a boy or girl for each child is assumed to be 0.5. The probability of having three boys and one girl (in any order) with four children can be calculated using the binomial probability formula:
P(X = k) = C(n, k) * p^k * (1-p)^(n-k)
Where P(X = k) is the probability of having k successes in n trials, C(n, k) is the number of combinations of n items taken k at a time, and p is the probability of a success on any given trial.
In this case, n = 4, k = 3, and p = 0.5. So, the calculation will be:
P(3 boys) = C(4, 3) * (0.5)^3 * (0.5)^(4-3)
P(3 boys) = 4 * (0.5)^3 * (0.5)^1
P(3 boys) = 4 * 0.125 * 0.5
P(3 boys) = 0.25 or 4/16
Therefore, the correct answer is b) 4/16.