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

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Question: A family has 2 children. What is the probability that both children are boys?

Options:

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

Correct Answer: 1/4

Solution: 

The possible combinations of children are BB, BG, GB, GG. Out of these, only 1 combination is both boys (BB). Thus, the probability is 1/4.

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

Practice Questions

Q1
A family has 2 children. What is the probability that both children are boys?
  1. 1/4
  2. 1/2
  3. 1/3
  4. 1/5

Questions & Step-by-Step Solutions

A family has 2 children. What is the probability that both children are boys?
Correct Answer: 1/4
  • Step 1: Understand that there are 2 children in the family.
  • Step 2: Recognize that each child can either be a boy (B) or a girl (G).
  • Step 3: List all possible combinations of the two children: BB (both boys), BG (boy and girl), GB (girl and boy), GG (both girls).
  • Step 4: Count the total number of combinations. There are 4 combinations: BB, BG, GB, GG.
  • Step 5: Identify how many of these combinations have both children as boys. There is only 1 combination: BB.
  • Step 6: Calculate the probability by dividing the number of favorable outcomes (1) by the total number of outcomes (4).
  • Step 7: The probability that both children are boys is 1/4.
  • Probability – Understanding the likelihood of an event occurring based on possible outcomes.
  • Combinatorics – The study of counting, arrangements, and combinations of objects.
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