A family has 2 children. What is the probability that both children are boys, given that at least one is a boy?
Practice Questions
1 question
Q1
A family has 2 children. What is the probability that both children are boys, given that at least one is a boy?
1/3
1/2
1/4
2/3
The possible combinations are BB, BG, GB. Given at least one is a boy, the combinations are BB, BG, GB. The probability of both being boys is 1/3.
Questions & Step-by-step Solutions
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Q
Q: A family has 2 children. What is the probability that both children are boys, given that at least one is a boy?
Solution: The possible combinations are BB, BG, GB. Given at least one is a boy, the combinations are BB, BG, GB. The probability of both being boys is 1/3.
Steps: 7
Step 1: Identify the possible combinations of two children. The combinations are: BB (both boys), BG (boy and girl), and GB (girl and boy).
Step 2: Since we know that at least one child is a boy, we can eliminate the combination where both are girls (GG).
Step 3: The remaining combinations are BB, BG, and GB. So, we have three possible combinations.
Step 4: Out of these combinations, we want to find the probability that both children are boys (BB).
Step 5: There is 1 combination (BB) that has both children as boys out of the 3 valid combinations (BB, BG, GB).
Step 6: To find the probability, we divide the number of favorable outcomes (1 for BB) by the total number of outcomes (3).
Step 7: Therefore, the probability that both children are boys, given that at least one is a boy, is 1/3.
