# How many Girls that play an Instrument are in the Sample?

• 300 students are asked, if they play a musical instrument.
• Half of the students asked were boys and half girls.
• 2/3 of students said they played a musical instrument. The rest did not play a musical insturment.
• 80 boys play an instrument.

The School want to interview a sample of 60 students on musical interests. How many girls that play a instrument will be in the sample?

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Problem is ill-defined. From data we know $200$ play, of whom $120$ must be girls. But this tells us nothing useful about the composition of the sample of $60$. If it is randomly chosen, one can say something about the expected (mean) number of girls who play an instrument, namely $(60)(1/2)(120/150)$, but the actual number is not determined. –  André Nicolas Mar 29 '12 at 11:00
Please use more descriptive titles. Imagine how the main page would look if all questions had titles like that. –  joriki Mar 29 '12 at 11:00
Andre Nicolas, try it now –  Leah Mar 29 '12 at 11:02
@Leah: The wording is clearer. Assume that the sample of $60$ is random. Here is a simple example that illustrates the issue. Question: A fair coin is tossed $10$ times. How many heads will there be? The mean number of heads is $5$. But the actual number might not be $5$. In fact, the probability of exactly $5$ is a bit under $25$%. In your problem, the mean number is $24$. But it is quite unlikely that the number will be exactly $24$. If the school chooses not randomly, but on the basis of sex (half and half) and then to represent musical interests, then yes, the answer is exactly $24$. –  André Nicolas Mar 29 '12 at 11:13

$\frac{2}{3}300=\color{red}{200}$ play an instrument. There are $\color{blue}{150}$ boys. Let's set it up like: $$\begin{matrix} &\text{boys}&\text{girls}&\text{total}\\ \text{ play}&80&120&\color{red}{200}\\ \text{don't}&70&30\\ \text{total}& \color{blue}{150} \end{matrix}$$
So on average you'll have $\frac{120}{300}\cdot 60= 24$ girls in your sample that play an instrument.