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?
Practice Questions
1 question
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?
0.75
0.5
0.25
0.6
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.
Questions & Step-by-step Solutions
1 item
Q
Q: 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?
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.
Steps: 5
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.
