Probability question

Question

An organization hires 20% of graduates from University A, 30% from University B and 50% from

University C. If 10% of graduates from University A, 20% of graduates from University B and 15% of

graduates from University C are exceptional, find:

1. The probability that the company will get an exceptional graduate

2. The probability that the company hires an exceptional graduate from University B

Answer 1

One way I like to use when dealing with percents and proportions is to just say I have 100 people total. So,

100 graduates: 20 from A, 30 from B, 50 from C.

Exceptional from A = 10% of 20, which is 2

Exceptional from B = 20% of 30, which is 6

Exceptional from C = 15% of 50, which is 7.5 (don't worry about the non-integer because it won't matter for calculating probabilities)

Probability that 1 selected at random is exceptional = all exceptional/100 = 15.5/100 = 0.155. This is simple probability.

Probability that 1 exceptional selected is from B = Probability of B given exceptional = 6/15.5 = 0.387. This is conditional probability, the condition being exceptional.