ruturaj
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?
24/91
45/91
2/3
67/91
84/91
Please explain the steps to be followed?
Another way to approach it:
Total jurors - 15
Men = 2/3 = 10
Women = 1/3 = 5
Jurors to be selected = 12
Men - atleast 2/3 = at least 8
Women - at most 1/3 = at most 4
The number of women selected can be 5 or less than 5. Less than 5 means at most 4. So if I find the probability of selecting 5 women and subtract it from 1, we will get the probability of selecting at most 4 women (the required probability)
Total number of ways of selecting the jurors = 15C12 = 15*14*13/3! = 455
Number of ways of selecting 5 women jurors (and 7 men) = 5C5 * 10C7 = 10*9*8/3! = 120
Probability of selecting 5 women jurors = 120/455 = 24/91
Probability of selecting at most 4 women jurors = 1 - 24/91 = 67/91