A physics class has 25 students, two of whom are Alex and Justin. Three students are chosen
uniformly at random for a lab demonstration. What is the probability that at least one of Alex
and Justin is chosen?
Options.
A) 0.3 B) 0.25 C) 0.19 D) 0.23 E) 0.2
We first calculate the probability that neither Alex nor Justin is chosen. The number   of ways to choose 3 people in the class is   􀀀25   3   . If neither Alex nor Justin can be chosen, there are   23 students that can be chosen and hence   􀀀23   3   ways to choose them. Therefore, the probability   that neither Alex nor Justin is chosen is   􀀀23   3   􀀀25   3   (=   23*22*21   3!   25*24*23   )=   23 *22 * 21/25 * 24 *23=   22 * 21/25 *24=   77/100,   so the probability that at least one of them is chosen is   1 -   77/100=   23/100= 
<gadget id="calculator">23/100</gadget>
<output>23/100 = around 0.23</output>
0.23   correct answer 0.23
<result>D</result>
A physics class has 25 students, two of whom are Alex and Justin. Three students are chosen
uniformly at random for a lab demonstration. What is the probability that at least one of Alex
and Justin is chosen?