Question

In an examination, 60 candidates passed Integrated Science or Mathematics. If 15 passed both subjects and 9 more passed Mathematics than Integrated Science, find the: (i) number of candidates who passed each subject. (ii) probability that a candidate passed exactly one subject.​

Answer 1

i) 42 candidates passed Mathematics, 33 candidates passed Science.

ii) There is a 75% chance that a candidate passed exactly one subject.

Explanation:

So we know that in total there are 60 candidates, and 15 passed both.

That leaves us with 45 candidates that passed either science or math. Since 9 more passed math than science, we see that out of those 45, 27 candidates passed math and 18 passed science. We add the 15 that got through both to each number, which means in total 42 candidates passed Mathematics, 33 candidates passed Science.

To see the probability, we know that 45 out of 60 only passed one subject. Simplified is 3/4 or 75%.