7. Find the indicated probability. Round to three decimal places.

Question

The participants in a television quiz show are picked from a large pool of

applicants with approximately equal numbers of men and women. Among

the last 11 participants there have been only 2 women. If participants are

picked randomly, what is the probability of getting 2 or fewer women when

11 people are picked?

a .033

b .006

c .032

d .027

Answer 1

the answer is a) .033

getting all males out of 11 picks would be probability = 1/2048

getting just one woman would be 11/2048

getting two women out of 11 would be 55/2048

getting 2 or less women would be 67/2048 = about 0.033 or 3.3% chance

Pascal's triangle, 12th row, add the 1st 3, divide by sum of the entire 12th row

1

11

121

1331

14641

15101051

1615201561

172135352171

18285670562881

19-36-84-126-126-84-36-9-1

1-10-45-120-210-252-210-120-45-10-1

1-11-55-165-330-462-462-330-165-55-11-1

(1+11+55)/2048 = 67/2048 = about 0.0327 = about 0.033

11C0 = 1

11C1 = 11

11C2 = 11!/9!2! = 55

Pr(W<2) = (11C0+11C1+11C2)/(sum of 11C0 through 11C11)