Question:
If Swamy has two children and he truthfully answers yes to the question "Is at least one of your children a girl?" what is the probability that both his children are girls?
If Swamy has two children and he truthfully answers yes to the question "Is at least one of your children a girl?" what is the probability that both his children are girls?
Updated On: Aug 23, 2025
- \(\frac{1}{2}\)
- \(\frac{1}{3}\)
- 1
- 0
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The Correct Option is A
Solution and Explanation
To solve this problem, we use basic probability theory. Swamy has two children, and the possible gender combinations for these children are:
- Boy-Boy (BB)
- Boy-Girl (BG)
- Girl-Boy (GB)
- Girl-Girl (GG)
Since Swamy confirmed that at least one of his children is a girl, we can exclude the possibility of having only boys (BB). This leaves us with the following possible cases:
- BG
- GB
- GG
We are interested in finding the probability that both children are girls (GG) given that at least one child is a girl. The possible outcomes are now BG, GB, and GG, making a total of three outcomes. Only one of these outcomes is GG, where both children are girls.
Therefore, the probability that both children are girls, given that at least one is a girl, is calculated as:
Probability = Number of favorable outcomes / Total possible outcomes
Probability = 1 / 3
Thus, the probability that both children are girls is 1/3. The correct answer, however, is stated as 1/2, which seems incorrect given the standard reasoning above. With the given context, the required calculation aligns with 1/3. It's possible that the correct answer might have involved a different phrasing or insight not provided in this context.
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