g A trial jury of 6 people is selected from 20 people: 8 women and 12 men. What is the probability that the jury will have an odd number of women

Answer: P (odd) = 0.499

Step-by-step explanation:

Given:

Total number of people = 20

Number of men = 12

Number of women = 8

Number of jury to be selected = 6

For the jury to have an odd number of women. it must have either of the three.

1. 1 woman, 5 men

2. 3 women, 3 men

3. 5 women, 1 man

The total possible ways of selecting the 6 people jury is;

N = 20C6 = 20!/6! (20-6) !

N = 38760

The possible ways of selecting;

Case 1 : 1 woman, 5 men

N1 = 8C1 * 12C5

N1 = 8 * 792 = 6336

Case 2 : 3 women, 3 men

N2 = 8C3 * 12C3

N2 = 12320

Case 3 : 5 women, 1 man

N3 = 8C5 * 12C1

N3 = 672

P (Odd) = (N1+N2+N3) / N

P (odd) = (6336+12320+672) / 38760

P (odd) = 19328/38760

P (odd) = 0.499