Statistic homework help

Question

A company has hired 12 new employees, and must assign 8 to the day shift and 4

to the night shift. Assume that they hired 7 men and 5 women.

(a) Find the number of ways that this can be done.

(b) Find the probability that all four of the night-shift employees are men?

(c) Find the probability that all four of the night-shift employees are women?

(d) Find the probability that at least one of the night-shift employees is a woman?

Answer 1

Ashley

(a) There are 12 people. Assuming nobody works two shifts we just have to choose 8 out of the 12 for the day shift (the other 4 automatically do the night shift). The number of ways we can choose 8 from 12 is

12 C 8 (which hopefully you can calculate on your calculator. If not n C r = n ! / ( r ! (n-r) !) with n=12, r=8

You should get 1995 8400

(b) Total possible outcomes = 1995 8400

How many do we have where night shift are all men ? Why how many ways can we choose the night shift if they are all men - well we can choose 4 men out of 7. So 7 C 4.

So our probability will be 7 C 4 / 19958400

(c) Idea here is similar to (b) - exercise for you

(d) Well if at least one of the night shift is a woman, we can't have 4 men on the nightshift, so the probability must be 1- p (we have 4 men on the nightshift). Exercise for you

Mike

Answer 2

There are C(12,4) ways that 4 of 12 can be selected for the night shift.

a)12*11*10*9/4! = 495

b) The number of ways that 4 men can be selected for the night shift is C(7, 4) = 35

35/495 = 7/99

c) The number of ways to choose 4 women is C(5,4) = 5

5/495 = 1/99

d) 1 - P(all are men) = 1 - 7/99 = 92/99