Final answer:
The probability of having three girls out of five children is computed by using the combinations formula to determine the different ways 3 girls can be chosen out of 5 children, and then multiplying that by the probability of each gender being born. The correct answer is 5/16.
Step-by-step explanation:
The question asks for the probability of having three daughters out of five offspring. The probability of having a girl in any single birth is 1/2. Since the genders of the children are independent events, we use the product rule and the combinations formula (nCr) to calculate this.
First, we find the number of ways to choose 3 girls out of 5 children, which is 5C3 (also written as ℒ5). Then, we multiply this number by the probability of having 3 girls and 2 boys, which is ½³ * ½². The number of ways 5C3 equals 10, and ½³ * ½² = 1/32, so we multiply these together: 10 * 1/32 = 10/32 = 5/16.
Therefore, the correct answer is B. 5/16.