Question 752938
<pre><b>
Student Scores:
<font color="red">53, 57, 59, 60, 60, 60, 61, 61, 62, 62, 62, 62, 63, 63, 65, 65, 65, 66, 67, 67,
68, 68, 68, 69, </font>71, 71, 71, 72, 72, 73, 73, 73, 73, 74, 74, 74, 75, 75, 75, 75,
75, 75, 75, 76, 76, 76, 76, 77, 77, 78, 78, 78, 78, 78, 79, 79, 79, 80, 81, 82,
82, 83, 84, 85, 85, 85, 86, 87, 88, 88, 88, 89, <font color="green">90, 93, 93, 94, 95, 95,</font> 96, 97
</pre>
If the passing score is 70 points and 5 students are picked at random, find the probability that:
<pre>
If I counted right, then there are 80 students, 24 fail and 56 pass,
and 6 are between 90 and 95.  I colored the failures red, and the
ones between 90 and 95 green.

a) all 5 fail

{{{C(24,5)/C(80,5)}}}{{{""=""}}}{{{42504/24040016}}} = 0.0017680521

b) only 2 fail

{{{(C(24,2)C(56,3))/C(80,5)}}}{{{""=""}}}{{{276*27720/24040016}}} = {{{7650720/24040016}}} = 0.3182493722

c) only 2 pass

{{{(C(56,2)C(24,3))/C(80,5)}}}{{{""=""}}}{{{1540*2024/24040016}}} = {{{3116960/24040016}}} = 0.1296571516

d) all 5 pass

{{{C(56,5)/C(80,5)}}}{{{""=""}}}{{{3819816/24040016}}} = 0.1588940706


e)their score is between 90 and 95 points

{{{C(6,5)/C(80,5)}}}{{{""=""}}}{{{6/24040016}}} = 0.0000002495838605

Edwin</pre>