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A student is selected at random from a group of students who study Mathematics a

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Question: A student is selected at random from a group of students who study Mathematics and Physics. If 70% study Mathematics and 40% study both subjects, what is the probability that a student studies Physics given that they study Mathematics?

Options:

  1. 0.4
  2. 0.3
  3. 0.5
  4. 0.6

Correct Answer: 0.4

Solution: 

Using the formula P(Physics|Mathematics) = P(Physics and Mathematics) / P(Mathematics) = 0.4 / 0.7 = 0.571.

A student is selected at random from a group of students who study Mathematics a

Practice Questions

Q1
A student is selected at random from a group of students who study Mathematics and Physics. If 70% study Mathematics and 40% study both subjects, what is the probability that a student studies Physics given that they study Mathematics?
  1. 0.4
  2. 0.3
  3. 0.5
  4. 0.6

Questions & Step-by-Step Solutions

A student is selected at random from a group of students who study Mathematics and Physics. If 70% study Mathematics and 40% study both subjects, what is the probability that a student studies Physics given that they study Mathematics?
  • Step 1: Understand the problem. We need to find the probability that a student studies Physics given that they study Mathematics.
  • Step 2: Identify the information given. We know that 70% of students study Mathematics (P(Mathematics) = 0.7) and 40% study both Mathematics and Physics (P(Physics and Mathematics) = 0.4).
  • Step 3: Use the formula for conditional probability. The formula is P(Physics|Mathematics) = P(Physics and Mathematics) / P(Mathematics).
  • Step 4: Substitute the values into the formula. We have P(Physics|Mathematics) = 0.4 / 0.7.
  • Step 5: Calculate the result. Divide 0.4 by 0.7 to get approximately 0.571.
  • Step 6: Interpret the result. This means that if a student studies Mathematics, there is about a 57.1% chance that they also study Physics.
  • Conditional Probability – The probability of an event occurring given that another event has already occurred.
  • Joint Probability – The probability of two events occurring simultaneously.
  • Total Probability – Understanding how to calculate probabilities based on given percentages.
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