A family has 2 children. What is the probability that both children are boys if
Practice Questions
Q1
A family has 2 children. What is the probability that both children are boys if it is known that at least one is a boy?
1/2
1/3
1/4
1/5
Questions & Step-by-Step Solutions
A family has 2 children. What is the probability that both children are boys if it is known 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), GB (girl and boy), GG (both girls).
Step 2: Since we know that at least one child is a boy, we can eliminate the combination GG (both girls).
Step 3: Now, we are left with three combinations: BB (both boys), BG (boy and girl), and GB (girl and boy).
Step 4: Out of these three combinations, we want to find the probability that both children are boys (BB).
Step 5: There is only 1 combination that is BB out of the 3 remaining 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 possible 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 scenario.
Elimination of Outcomes – Removing certain outcomes based on given conditions to refine the sample space.
