Question

Suppose 60% of all college professors like tennis, 65% like bridge, and 50% like chess; 45% like any given pair of recreations.

(a) Should you be suspicious if told 20% like all three recreations?
(b) What is the smallest percentage who could like all three recreations?

Answer 1

a) yes we should get suspicious

b) smallest percentage to like all three sports= 60

Explanation:

Let the total professors be =100

n(tennis) = 60

n( bridge) = 65

n( chess)= 50

n( T U B) = 45, n(BU C) = 45, n(T UC)=45

n( T U B U C)= n(T) + n(B) + n(C) - n( T U B) - n( BU C) - n(TUC) +
`n(T\cap B\cap C)`

100 = 60 + 65 + 50 - 45-45-45 +
`n(T\cap B\cap C)`

`n(T\cap B\cap C)` = 60

Therefore,

a) yes we should get suspicious

b) smallest percentage to like all three sports= 60