Question

A survey of students showed 10% were dissatisfied with their lunch. Half of the complaints came from students who ate at the cafeteria, which served 40% of all lunches. Find the probability that a student was unhappy with their lunch given that they ate in the cafeteria

Answer 1

We have

40% of all lunches are served by cafeteria

And 10% of students are dissatisfied with their lunch , half of the complaints came from students who ate at cafeteria.

i.e. 10%*0.5 = 5% complaints are from students who ate at cafeteria.

Thus

Probability that a student was unhappy with their lunch given that they ate in the cafeteria is

= P(complaints from students who ate at cafeteria)/ P(Lunch served by cafeteria)

= 5%/40%

=0.05/.4

= 0.125

Thus probability that a student was unhappy with their lunch given that they ate in the cafeteria is 0.125