In a family with 3 children, what is the probability that at least one of them is a girl?
Practice Questions
1 question
Q1
In a family with 3 children, what is the probability that at least one of them is a girl?
1/8
1/2
7/8
3/8
The only scenario where there are no girls is if all three children are boys, which has a probability of (1/2)^3 = 1/8. Therefore, the probability of having at least one girl is 1 - 1/8 = 7/8.
Questions & Step-by-step Solutions
1 item
Q
Q: In a family with 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 three children are boys, which has a probability of (1/2)^3 = 1/8. Therefore, the probability of having at least one girl is 1 - 1/8 = 7/8.
Steps: 6
Step 1: Understand that each child can either be a boy (B) or a girl (G).
Step 2: Since there are 3 children, we can have combinations of boys and girls.
Step 3: The only scenario where there are no girls is if all three children are boys (BBB).
Step 4: Calculate the probability of having all boys. Each child has a 1/2 chance of being a boy, so for 3 children, the probability is (1/2) * (1/2) * (1/2) = (1/2)^3 = 1/8.
Step 5: To find the probability of having at least one girl, we subtract the probability of having all boys from 1. So, we calculate 1 - (1/8) = 7/8.
Step 6: Therefore, the probability that at least one of the three children is a girl is 7/8.
