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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.
Answer
P(M and P) =
P(M) x P(P).
So
So a2 – 35a + 150 = 0,
So (a - 30)(a - 5) = 0,
a > 5, so a = 30, b = 5.
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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