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?
1/4
1/3
1/2
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.
