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?
Practice Questions
1 question
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?
0.4
0.3
0.5
0.6
Using the formula P(Physics|Mathematics) = P(Physics and Mathematics) / P(Mathematics) = 0.4 / 0.7 = 0.571.
Questions & Step-by-step Solutions
1 item
Q
Q: 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?
Solution: Using the formula P(Physics|Mathematics) = P(Physics and Mathematics) / P(Mathematics) = 0.4 / 0.7 = 0.571.
Steps: 6
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.
