A family has 3 children. What is the probability that at least one of them is a
Practice Questions
Q1
A family has 3 children. What is the probability that at least one of them is a girl?
1/8
1/4
3/4
7/8
Questions & Step-by-Step Solutions
A family has 3 children. What is the probability that at least one of them is a girl?
Correct Answer: 7/8
Step 1: Understand that there are 3 children in the family.
Step 2: Recognize that each child can either be a boy (B) or a girl (G).
Step 3: Calculate the total number of possible combinations of boys and girls for 3 children. There are 2 options (B or G) for each child, so the total combinations are 2^3 = 8.
Step 4: List the possible combinations: BBB, BBG, BGB, BGG, GBB, GBG, GGB, GGG.
Step 5: Identify the scenario where there are no girls, which is 'BBB' (all boys).
Step 6: Calculate the probability of having all boys. Since there is 1 way to have all boys out of 8 total combinations, the probability is 1/8.
Step 7: To find the probability of having at least one girl, subtract the probability of all boys from 1: 1 - (1/8) = 7/8.
Step 8: Conclude that the probability of having at least one girl is 7/8.
Probability of Independent Events – The question tests the understanding of calculating probabilities for independent events, specifically the complementary probability of having at least one girl among three children.
Complementary Probability – The solution demonstrates the use of complementary probability, where the probability of at least one event occurring is found by subtracting the probability of the event not occurring from 1.
