Answer:
The probability that exactly 10 of these are from the second section is 0.217.
Step-by-step 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:
[tex]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[/tex]
