Question

An instructor who taught two sections of engineering statistics last term, the first with 25 students and the second with 40, decided to assign a term project. After all projects had been turned in, the instructor randomly ordered them before grading. Consider the first 15 graded projects. (a) What is the probability that exactly 10 of these are from the second section

Answer 1

The probability that exactly 10 of these are from the second section is 0.217.

Explanation:

This is a problem of combinatorics, we have to count how many different ways of taking 15 projects out of 65 (total number of projects=25+40), which is going to be our total number of cases, and then we have to count how many different ways of taking 10 out of 40 (second section) and 5 (15 (number of graded projects)-10 (taken from second section) out of 25 (first section), which is the number of cases that fulfill our probability.

Doing the calculations:

`P_{\mbox{10 from second section}} =\frac{\mbox{cases that fulfill}}{\mbox{total cases}} =\frac{\left(\begin{array}{ccc}25\\5\end{array}\right)*\left(\begin{array}{ccc}40\\10\end{array}\right)}{\left(\begin{array}{ccc}65\\15\end{array}\right)} =0.217`