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Consider a hypothetical example.

In a school, there are three classes, 1st grade class, 2nd grade class, and 3rd grade class. In each class, there are 3 students with roll numbers $1$, $2$, and $3$. Suppose you want to estimate the average IQ of students of the school. For that you want to select roll number $1$ from 1st grade class; roll number $2$ from 2nd grade class; and roll number $3$ from 3rd grade class.

Now suppose all $9$ students of the school stand randomly in a row. If you randomly select a student, what is the probability that the student has $i$th roll number from $i$th grade class, where $i=1,2,3$?

Is the probability that the student has $i$th roll number from $i$th grade class, where $i=1,2,3$ simply $\frac{1}{9}$?

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  • $\begingroup$ are you asking what's the prob that a randomly chosen student out of the 9 is one of the 3 specified in the 1st paragraph? If so, it's 1/3. $\endgroup$ – spaceisdarkgreen Jan 3 '17 at 5:20
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There are $3$ students that meet the criteria you're looking for. If you choose $1$ at random from the $9$ students, there is $1/3$ probability you get one of the $3$ students.

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Case 1-

Student selected has roll number 1 and from class 1.

Then probability = $\frac19$

Case 2-

Student selected has roll number 2 and from class 2.

Then probability = $\frac19$

Case 3-

Student selected has roll number 3 and from class 3.

Then probability = $\frac19$

Adding all 3 cases

Probability = $\frac19 + \frac19 + \frac19 = \frac39 $

= $ \frac13$

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