In a family of 4 children, what is the probability that at least one is a girl g

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Question: 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?

Options:

Correct Answer: 3/4

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.

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?

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?

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).
Step 8: The probability is 2/3.

Conditional Probability – The probability of an event occurring given that another event has already occurred.
Combinatorial Analysis – Understanding the different combinations of boys and girls in a family of 4 children.