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If you have 10 questions to be asked in an exam : 5 from biology and 5 from chemistry. Each module has 10 lectures. What is the probability that a particular lecture will be asked in the exam ?

Basically :

  • 2 Modules : Chemistry, Biology
  • 10 lectures each module
  • 10 questions in Exam, 5 from each lecture of each module
  • What are the chances for each lecture that might be asked in the exam ?

For example, what is the chance that one of the 10 lectures from Biology will make it to the 5 questions asked in the exam ?

Would like a simple walkthrough to the solution. This is not homework, just thought of it and cannot get it right.

I said 1/5 * 10 = 2 .. does that mean 20% chance ? I can't be sure.

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What's the relationship between questions and lectures? Didn't understand it from the question, sorry. – gt6989b Mar 4 '13 at 22:42
For one lecture, the probability will be 5 out of 10, which is 50%. – karakfa Mar 4 '13 at 22:47
Okay i'll make it simpler please read question in 1 minute. – NLed Mar 4 '13 at 22:47
Are you assuming that the probability of a lecture being in the test is uniformaly distributed ? – Belgi Mar 4 '13 at 22:53
@Belgi not sure, this is an actual example of my exams. – NLed Mar 4 '13 at 23:29
up vote 0 down vote accepted

If we consider biology alone, there are $10 \choose 5$ ways of picking 5 from the 10 lectures. Out of these total number of ways, we need to figure in how many, a particular lecture, say $L$ will be present. If $L$ is sure to be asked, the remaining 4 questions could be picked from 9 lectures in $9 \choose 4$ ways. Thus the probability of a particular lecture $L$ appearing in the exam is $\frac{9 \choose 4}{10 \choose 5}=0.5$.

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What's the percentage then ? – NLed Mar 4 '13 at 23:28
@NLed: 50%, exact... – Bravo Mar 4 '13 at 23:37
@NLed: Or even simply, the teacher has 10 lectures and is equally likely to choose between them for her 5 qs, so the probability of one lecture appearing in the exam is 5/10=0.5. – Bravo Mar 4 '13 at 23:39

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