Question

The probability that a student passes an examination is 2/5. If two students are picked at random from the class, what is the probability that one of them will pass and the other one will fail?

Answer 1

Answer:

12/25

Step-by-step explanation:

There are four possibilities, P=Pass, F=Fail:

The chance of failing is 1-2/5 = 3/5.

PP = 2/5 * 2/5  = 4/25

PF = 2/5 * 3/5 = 6/25

FP = 3/5 * 2/5 = 6/25

FF = 3/5 * 3/5 = 9/25

(note that these chances add up to 1, as they should!)

We are interested in PF or FP, the sum of those is 6/25 + 6/25 = 12/25

So generally, when you say "AND" you multiply chances, and when you say "OR" you add them.

So (student 1 Passes AND student 2 Fails) OR (Student 1 Fails AND student 2 Passes)