A family has 3 children. What is the probability that at least one of them is a girl?
Practice Questions
1 question
Q1
A family has 3 children. What is the probability that at least one of them is a girl?
1/8
1/4
3/4
7/8
The only scenario where there are no girls is if all are boys. The probability of all boys is (1/2)^3 = 1/8. Therefore, the probability of at least one girl is 1 - 1/8 = 7/8.
Questions & Step-by-step Solutions
1 item
Q
Q: A family has 3 children. What is the probability that at least one of them is a girl?
Solution: The only scenario where there are no girls is if all are boys. The probability of all boys is (1/2)^3 = 1/8. Therefore, the probability of at least one girl is 1 - 1/8 = 7/8.
Steps: 8
Step 1: Understand that there are 3 children in the family.
Step 2: Recognize that each child can either be a boy (B) or a girl (G).
Step 3: Calculate the total number of possible combinations of boys and girls for 3 children. There are 2 options (B or G) for each child, so the total combinations are 2^3 = 8.
Step 4: List the possible combinations: BBB, BBG, BGB, BGG, GBB, GBG, GGB, GGG.
Step 5: Identify the scenario where there are no girls, which is 'BBB' (all boys).
Step 6: Calculate the probability of having all boys. Since there is 1 way to have all boys out of 8 total combinations, the probability is 1/8.
Step 7: To find the probability of having at least one girl, subtract the probability of all boys from 1: 1 - (1/8) = 7/8.
Step 8: Conclude that the probability of having at least one girl is 7/8.
