Answer to Question #205619 in Statistics and Probability for Ethan Wong

Question

In a group of 50 students, 40 students study Math, 32 study Physics and each student studies at least one of the subjects. Use this information to answer the questions below

2d) If a student is randomly selected, what is the probability that the student studies Math given that he or she DOES NOT study Physics?

Answer 1

$$N(A\cup M)=50$$

$$N(A)=40, N(B)=32$$

$$N(A\cap B)=N(A)+N(B)-N(A\cup B)$$

$$=40+32-50=22$$

$$N(A\cap B')=40-22=18$$

$$N(B\cap A')=32-22=10$$

$$P(B|A')=1$$

The probability that the student studies Math given that he or she DOES NOT study Physics is 1.