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In a family with 3 children, what is the probability that at least one child is

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Question: In a family with 3 children, what is the probability that at least one child is a girl given that at least one child is a boy?

Options:

  1. 0.75
  2. 0.5
  3. 0.25
  4. 0.6

Correct Answer: 0.75

Solution: 

The total outcomes for 3 children are 8. The outcomes with at least one boy are 7. The outcomes with at least one girl and one boy are 6. Thus, P(Girl|Boy) = 6/7 ≈ 0.857.

In a family with 3 children, what is the probability that at least one child is

Practice Questions

Q1
In a family with 3 children, what is the probability that at least one child is a girl given that at least one child is a boy?
  1. 0.75
  2. 0.5
  3. 0.25
  4. 0.6

Questions & Step-by-Step Solutions

In a family with 3 children, what is the probability that at least one child is a girl given that at least one child is a boy?
  • Step 1: Identify the total number of outcomes for 3 children. Each child can be either a boy (B) or a girl (G). So, the possible combinations are: BBB, BBG, BGB, BGG, GBB, GBG, GGB, GGG. This gives us a total of 8 outcomes.
  • Step 2: Determine the outcomes that have at least one boy. The only combination that does not have a boy is GGG. Therefore, the outcomes with at least one boy are: BBB, BBG, BGB, BGG, GBB, GBG, GGB. This gives us 7 outcomes.
  • Step 3: Now, find the outcomes that have at least one girl and one boy. The combinations that fit this criteria are: BBG, BGB, BGG, GBB, GBG, GGB. This gives us 6 outcomes.
  • Step 4: Calculate the probability of having at least one girl given that there is at least one boy. This is done by taking the number of outcomes with at least one girl and one boy (6) and dividing it by the total outcomes with at least one boy (7). So, P(Girl|Boy) = 6/7.
  • Step 5: Convert the fraction to a decimal to find the probability. 6/7 is approximately 0.857.
  • 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 experiment.
  • Counting Outcomes – Understanding how to count favorable outcomes versus total outcomes in probability.
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