Problem 1 A company decides to downsize its staff. It has 30 people presently (1

Question

Problem 1 A company decides to downsize its staff. It has 30 people presently (12 women and 18 men), and wants to lay off 10. Let x number of women laid off. Set up a probability model for the situation, and note the possible values of X What is the probability that X-87 Is this unusual? How many women should we expect to be laid off? Does this also indicate that 8 is unusual? Problem 15 In a shipment of 15 microchips, 2 are defective and 13 are not defective. A sample of three microchips is chosen at random. Find the probability that (a) all three microchips are not defective, (b) one microchip is defective Be sure to set up the model, as well as state the possible values of x.

Explanation / Answer

Total number of ways to lay off 10employes out of 30 = C(30,10) = 30045015

Total number of ways to lay off 8 women and 2 men = C(12,8)*C(18,2) = 495*153 = 75735

P(layoff 8 women) = 75735/30045015 = 0.00252, yes laying off 8 women is unusual. If the process is random the probablity is low 0.00252 hence unusual

b)

Expected women to be laid off

P(individual being laid off) = 10/30 = 1/3

E(women laid off) = 12/3 = 4

PS: We are directed to solve only 1st question if multiple questions are posted

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