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In a class of 40 students, 25 are taking Mathematics, 15 are taking Physics, and

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Question: In a class of 40 students, 25 are taking Mathematics, 15 are taking Physics, and 10 are taking both. What is the probability that a student is taking Physics given that they are taking Mathematics?

Options:

  1. 1/4
  2. 1/3
  3. 1/2
  4. 1/5

Correct Answer: 1/2

Solution: 

P(Physics | Mathematics) = P(Physics and Mathematics) / P(Mathematics) = 10/25 = 2/5.

In a class of 40 students, 25 are taking Mathematics, 15 are taking Physics, and

Practice Questions

Q1
In a class of 40 students, 25 are taking Mathematics, 15 are taking Physics, and 10 are taking both. What is the probability that a student is taking Physics given that they are taking Mathematics?
  1. 1/4
  2. 1/3
  3. 1/2
  4. 1/5

Questions & Step-by-Step Solutions

In a class of 40 students, 25 are taking Mathematics, 15 are taking Physics, and 10 are taking both. What is the probability that a student is taking Physics given that they are taking Mathematics?
  • Step 1: Identify the total number of students in the class, which is 40.
  • Step 2: Identify how many students are taking Mathematics, which is 25.
  • Step 3: Identify how many students are taking Physics, which is 15.
  • Step 4: Identify how many students are taking both Mathematics and Physics, which is 10.
  • Step 5: To find the probability that a student is taking Physics given that they are taking Mathematics, we need to use the formula: P(Physics | Mathematics) = P(Physics and Mathematics) / P(Mathematics).
  • Step 6: Calculate P(Physics and Mathematics), which is the number of students taking both subjects, so it is 10.
  • Step 7: Calculate P(Mathematics), which is the total number of students taking Mathematics, so it is 25.
  • Step 8: Substitute the values into the formula: P(Physics | Mathematics) = 10 / 25.
  • Step 9: Simplify the fraction 10 / 25 to get 2 / 5.
  • Conditional Probability – The probability of an event occurring given that another event has already occurred.
  • Set Theory – Understanding the relationships between different groups (sets) of students taking various subjects.
  • Inclusion-Exclusion Principle – A principle used to calculate the size of the union of two sets, which is relevant for determining the number of students taking both subjects.
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