If a jury of 12 people is to be selected randomly from a pool of 15 potential jurors, and the jury pool consists of 2/3 men and 1/3 women, what is the probability that the jury will comprise at least 2/3 men? Pick one:
A) 24/91
B) 45/91
C) 2/3
D) 67/91
E) 84/91
We have a pool of 10 men and 5 women   We need a jury of 12 people   What is the probability that the jury will comprise at least 2/3 men?   2/3 of a jury of 12 = 8 men. There will always be at least 8 men on the jury unless all 5 women are selected, in that case there will be 7 men and 5 women.   15C12 = 455 ways to select a jury of 12 from a pool of 15   5C5 = 1 way to select all 5 women   10C7 = 120 ways to select 7 men from a pool of 10   1*120= 
<gadget id="calculator">1*120</gadget>
<output>120</output>
120 ways to select a jury with fewer than 8 men   (455-120)/455= 335/455 = 67/91   Answer 67/91
<result>D</result>
If a jury of 12 people is to be selected randomly from a pool of 15 potential jurors, and the jury pool consists of 2/3 men and 1/3 women, what is the probability that the jury will comprise at least 2/3 men?