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A family has 2 children. What is the probability that both children are boys if

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Question: A family has 2 children. What is the probability that both children are boys if it is known that at least one is a boy?

Options:

  1. 1/2
  2. 1/3
  3. 1/4
  4. 1/5

Correct Answer: 1/3

Solution: 

The possible combinations of children are BB, BG, GB, GG. Given that at least one is a boy, we can eliminate GG, leaving us with BB, BG, GB. Out of these 3 combinations, only 1 is BB. Therefore, the probability is 1/3.

A family has 2 children. What is the probability that both children are boys if

Practice Questions

Q1
A family has 2 children. What is the probability that both children are boys if it is known that at least one is a boy?
  1. 1/2
  2. 1/3
  3. 1/4
  4. 1/5

Questions & Step-by-Step Solutions

A family has 2 children. What is the probability that both children are boys if it is known that at least one is a boy?
  • Step 1: Identify the possible combinations of two children. The combinations are: BB (both boys), BG (boy and girl), GB (girl and boy), GG (both girls).
  • Step 2: Since we know that at least one child is a boy, we can eliminate the combination GG (both girls).
  • Step 3: Now, we are left with three combinations: BB (both boys), BG (boy and girl), and GB (girl and boy).
  • Step 4: Out of these three combinations, we want to find the probability that both children are boys (BB).
  • Step 5: There is only 1 combination that is BB out of the 3 remaining 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 possible outcomes (3).
  • Step 7: Therefore, the probability that both children are boys, given that at least one is a boy, is 1/3.
  • Conditional Probability – The probability of an event occurring given that another event has already occurred.
  • Sample Space – The set of all possible outcomes in a probability scenario.
  • Elimination of Outcomes – Removing certain outcomes based on given conditions to refine the sample space.
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