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In a family with 3 children, what is the probability that at least one of them i

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Question: In a family with 3 children, what is the probability that at least one of them is a girl?

Options:

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

Correct Answer: 7/8

Solution: 

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

In a family with 3 children, what is the probability that at least one of them i

Practice Questions

Q1
In a family with 3 children, what is the probability that at least one of them is a girl?
  1. 1/8
  2. 1/2
  3. 7/8
  4. 3/8

Questions & Step-by-Step Solutions

In a family with 3 children, what is the probability that at least one of them is a girl?
  • Step 1: Understand that each child can either be a boy (B) or a girl (G).
  • Step 2: Since there are 3 children, we can have combinations of boys and girls.
  • Step 3: The only scenario where there are no girls is if all three children are boys (BBB).
  • Step 4: Calculate the probability of having all boys. Each child has a 1/2 chance of being a boy, so for 3 children, the probability is (1/2) * (1/2) * (1/2) = (1/2)^3 = 1/8.
  • Step 5: To find the probability of having at least one girl, we subtract the probability of having all boys from 1. So, we calculate 1 - (1/8) = 7/8.
  • Step 6: Therefore, the probability that at least one of the three children is a girl is 7/8.
  • Probability of Independent Events – The question tests the understanding of calculating probabilities for independent events, specifically the probability of having at least one occurrence of an event (having a girl) in multiple trials (children).
  • Complement Rule – The solution utilizes the complement rule, which states that the probability of at least one event occurring is equal to one minus the probability of the event not occurring at all.
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