MSV 25: The Independent School

In a small school of 60 students, 15 study maths but not physics, and 10 study physics but not maths.

More than half the school studies either maths or physics (or both). The events ‘a student studies maths’ and ‘student studies physics’ are independent. Complete the Venn diagram.

P(M and P) = P(M) x P(P). So So a 2 – 35a = 0, So (a - 30)(a - 5) = 0, a > 5, so a = 30, b = 5. Answer

Here you are given a school of unknown size. You know, however, that the events ‘a random student studies maths’ and ‘a random student studies physics’ are independent. What is the simplest possible connection you can find between a, b, c and d?

Answer

You are given a small school of 60 students, where students study maths, physics and chemistry as above. The events M and P are independent, the events P and C are independent, and the events C and M are also independent. Complete the Venn diagram.

So s = 12, r = 8, t = 6. Answer

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