A family has 2 children. What is the probability that both children are boys, gi

A family has 2 children. What is the probability that both children are boys, given that at least one is a boy?

A family has 2 children. What is the probability that both children are boys, given that at least one is a boy?

Step 1: Identify the possible combinations of two children. The combinations are: BB (both boys), BG (boy and girl), and GB (girl and boy).
Step 2: Since we know that at least one child is a boy, we can eliminate the combination where both are girls (GG).
Step 3: The remaining combinations are BB, BG, and GB. So, we have three possible combinations.
Step 4: Out of these combinations, we want to find the probability that both children are boys (BB).
Step 5: There is 1 combination (BB) that has both children as boys out of the 3 valid combinations (BB, BG, GB).
Step 6: To find the probability, we divide the number of favorable outcomes (1 for BB) by the total number of outcomes (3).
Step 7: Therefore, the probability that both children are boys, given that at least one is a boy, is 1/3.

Conditional Probability – The probability of an event occurring given that another event has already occurred.
Sample Space – The set of all possible outcomes in a probability experiment.
Combinatorial Analysis – The study of counting, arrangement, and combination of objects.