MediumMathematicsHigh School (11–12)Statistics and Probability › ProbabilityNumerical

In a survey of 60 students, 34 said they play a musical instrument, 27 said they take an art club…

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

In a survey of $60$ students, $34$ said they play a musical instrument, $27$ said they take an art club, and $12$ said they do both. Find four numbers. How many students do at least one of the two? How many do neither? How many do exactly one? How many play an instrument but do not take the art club?

Need a reminder? The key ideaShow

Use $n(A \cup B) = n(A) + n(B) - n(A \cap B)$ , $n(A - B) = n(A) - n(A \cap B)$ and $n(A') = n(S) - n(A)$ . For three events add the three singles, take away the three pairs and add the triple. De Morgan: $(A \cup B)' = A' \cap B'$ .

The worked solution

Have you tried it?

Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

← All Problems

← A card is drawn from an ordinary pack of 52 cards…A school has 100 members in three clubs… →

More onStatistics and Probability › Probability

Discussion (0)

Loading…