In a family of 4 children, what is the probability that at least one is a girl given that there are at least 2 boys?
Practice Questions
1 question
Q1
In a family of 4 children, what is the probability that at least one is a girl given that there are at least 2 boys?
1/2
3/4
1/4
2/3
If there are at least 2 boys, the possible combinations are (2B, 2G), (3B, 1G), (4B). Thus, the probability of having at least one girl is 3/4.
Questions & Step-by-step Solutions
1 item
Q
Q: In a family of 4 children, what is the probability that at least one is a girl given that there are at least 2 boys?
Solution: If there are at least 2 boys, the possible combinations are (2B, 2G), (3B, 1G), (4B). Thus, the probability of having at least one girl is 3/4.
Steps: 8
Step 1: Understand the family has 4 children.
Step 2: Identify the condition given: there are at least 2 boys.
Step 3: List the possible combinations of boys (B) and girls (G) given at least 2 boys: (2B, 2G), (3B, 1G), and (4B).
Step 4: Count the total combinations listed: (2B, 2G), (3B, 1G), (4B) = 3 combinations.
Step 5: Identify which of these combinations have at least one girl: (2B, 2G) and (3B, 1G) both have girls.
Step 6: Count the combinations with at least one girl: (2B, 2G) and (3B, 1G) = 2 combinations.
Step 7: Calculate the probability of having at least one girl given at least 2 boys: Number of combinations with at least one girl (2) divided by total combinations (3).
