# Probability of any given student being chosen in this question

This question from my textbook

Three high schools have senior classes of size 100, 400, 500. Scheme A: make a list of all 1000 students and choose one randomly; Scheme B: pick a school at random then a student at random;

Makes the comparison by showing that choosing a student from one of the high-schools is different across the two schemes

In Scheme A each person in first school is chosen with probability 1/1000; in Scheme B choose that school 1/3 of the time, and then each person is chosen 1/100 of the time, so a person in the first school is now chosen 1/300 of the time.

I did not think to use a single school as an example and wanted to solve this question by showing that in general the probability of choosing any student from any school is different.

How would I calculate the probability of choosing any particular student in scheme B?

I tried drawing a tree diagram where I had $\frac{1}{3}$ probability for choosing each school and then $\frac{1}{100}$, $\frac{1}{400}$, $\frac{1}{500}$ for choosing a student from each school respectively.

Is this a correct start?

• So the probability is then the sum of probabilitoes for each school? $\frac{1}{300}+\frac{1}{1200}+\frac{1}{1500} = \frac{29}{6000}$ – EvaD Oct 5 '17 at 13:14
• The probability of what? The probability that some student is chosen has to be $1$. This is a good check of your arithmetic. In fact $100 \cdot \frac 1{300}+400 \cdot \frac 1{1200}+500 \cdot \frac 1{1500}=1$. What you have shown is that the chance of an individual student from C being selected if $\frac 15$ of the chance that an individual student from A is selected That is what you were looking to show. – Ross Millikan Oct 5 '17 at 14:26
• I am trying to find the probability of any given student being selected using scheme B. By scheme A $P(student) = \frac{1}{1000}$, by scheme B I am asking if it is correct that $P(student) = P(student | school A) + P(student| school B) + P(student| school C)$ – EvaD Oct 5 '17 at 14:39