Question 388629
3) A class has 28 students. There are 5 good students, 13 fairly good students and 10 medium students. Randomly take 4 students to attend the meeting. Find the probability to have at least 2 good students that was chosen.
<pre>
The denominator of the desired probability is 28 choose 4 or 28C4.

It is easier to get the probability of the complement event and then 
subtract from 1.

The complement event is that either 

A. all 4 students were chosen from the 13+10 or 23 non-good students

or

B. 1 good student was chosen from the 5 and the other 3 were chosen from
   the 23 non-good students.

P(A or B) = P(A)+P(B) = {{{23C4/(28C4)}}} + {{{(5C1/(28C4))*(23C3/(28C4))}}}

=  {{{8855/20475}}} + {{{(5/20475)*(1771/(20475))}}} = 0.4324997548

That's the probability of the complement event.

The desired probability is therefore 1 - 0.4324997548 = 0.5675002452

Edwin</pre>