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  • 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.2012-03-29
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    Please use more descriptive titles. Imagine how the main page would look if all questions had titles like that.2012-03-29
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    Andre Nicolas, try it now2012-03-29
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    @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 $24$.2012-03-29

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