Suppose there are 1000 first-year students at a certain university.

Question

Two hundred are taking French but not statistics, one hundred are taking statistics but not French, and another 50 are taking both French and statistics. If you pick a student at random, find the following probabilities:

A) P(is taking French)

B) P(is taking French or statistics)

C) P(is not taking French)

D) P(is taking neither French nor statistics)

Answer 1

F = taking French

S = taking Statistics

 

n₁ = 200 students taking French, but not Statistics

n₂ = 100 students taking Statistics, but not French

n₃ = 50 students taking both French and Statistics

 

A)  P(is taking French) = P(F) = 200/1000 = 0.2

 

The probability of students taking French is 0.2.

 

B)  P(is taking French or Statistics) = P(F or S) = P(F) + P(S) - P(F and S) = 200/1000 + 100/1000 - 50/1000 = 250/1000 = 0.25

 

The probability of students taking either French or Statistics is 0.25.

 

C)  P(is not taking French) = P(F^c) = 1 - P(F) = 1 - 0.2 = 0.8

 

The probability of students not taking French is 0.8.

 

D)  P(is taking neither French nor Statistics) = P(F^c and S^c) = P(F^c)*P(S^c) = (0.8)(0.9) = 0.72

 

The probability of students taking neither French nor Statistics is 0.72.