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In a group of 100 people, 60 like football, 30 like basketball, and 10 like both

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Question: In a group of 100 people, 60 like football, 30 like basketball, and 10 like both. What is the probability that a person likes football given that they like basketball?

Options:

  1. 0.5
  2. 0.3
  3. 0.6
  4. 0.7

Correct Answer: 0.6

Solution: 

Using conditional probability, P(Football | Basketball) = P(Football and Basketball) / P(Basketball) = 10/30 = 1/3.

In a group of 100 people, 60 like football, 30 like basketball, and 10 like both

Practice Questions

Q1
In a group of 100 people, 60 like football, 30 like basketball, and 10 like both. What is the probability that a person likes football given that they like basketball?
  1. 0.5
  2. 0.3
  3. 0.6
  4. 0.7

Questions & Step-by-Step Solutions

In a group of 100 people, 60 like football, 30 like basketball, and 10 like both. What is the probability that a person likes football given that they like basketball?
  • Step 1: Identify the total number of people in the group, which is 100.
  • Step 2: Identify how many people like basketball, which is 30.
  • Step 3: Identify how many people like both football and basketball, which is 10.
  • Step 4: Calculate the probability of a person liking both football and basketball, which is P(Football and Basketball) = 10/100.
  • Step 5: Calculate the probability of a person liking basketball, which is P(Basketball) = 30/100.
  • Step 6: Use the formula for conditional probability: P(Football | Basketball) = P(Football and Basketball) / P(Basketball).
  • Step 7: Substitute the values: P(Football | Basketball) = (10/100) / (30/100).
  • Step 8: Simplify the equation: P(Football | Basketball) = 10/30.
  • Step 9: Further simplify to get P(Football | Basketball) = 1/3.
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