My Learning Cart
?
Categories
Account

A family has 3 children. What is the probability that at least one of them is a

₹0.0
Login to Download
  • 📥 Instant PDF Download
  • ♾ Lifetime Access
  • 🛡 Secure & Original Content

What’s inside this PDF?

Question: A family has 3 children. What is the probability that at least one of them is a girl?

Options:

  1. 1/8
  2. 1/4
  3. 3/4
  4. 7/8

Correct Answer: 7/8

Solution: 

The only scenario where there are no girls is if all are boys. The probability of all boys is (1/2)^3 = 1/8. Therefore, the probability of at least one girl is 1 - 1/8 = 7/8.

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. 1/8
  2. 1/4
  3. 3/4
  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.
Soulshift Feedback ×

On a scale of 0–10, how likely are you to recommend The Soulshift Academy?

Not likely Very likely
Home Practice Performance eBooks