Inconclusive Survey
Probability
Level
2
In a survey of 2000 people, 68% of the respondents were male and the remaining 32% were female. If 65% of the respondents had maths degrees, what is the minimum number of males with maths degrees?
Impossible to tell (minimum
)
816
660
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1 solution
Firstly note that as we do not know how the mathematics graduates are distributed among the males and females, we cannot just multiply the percentages together.
In total we know that there are 2 0 0 0 × 0 . 6 5 = 1 3 0 0 mathematics graduates.
These 1 3 0 0 mathematics graduates are either male or female. This means the minimum number of male mathematics graduates will happen when there is the maximum number of female mathematics graduates.
The maximum number of female mathematics graduates would happen if all of the female respondents were mathematics graduates. The number of female respondents is: 2 0 0 0 × 0 . 3 2 = 6 4 0 .
So, the minimum number of male mathematics graduates is therefore 1 3 0 0 − 6 4 0 = 6 6 0 .
Extensions
What is the maximum number of male maths graduates?
What is the minimum number of female mathematics graduates?
Which more likely: that a randomly selected male is a mathematics graduate, or that a randomly selected female is a mathematics graduate?