A stockroom clerk returns three safety helmets at random to three steel mill employees who had previous checked them. If Gary, Yuri and Cris, in that order, receive one of the three hats, list all the sample points for the possible orders of returning the helmets, and find the values of random variable X representing the number of correct matches. *

Solution:

Let the helmets which Gary, Yuri and Cris had checked in previously be denoted as G, Y and C. As the helmets are received in the order of Gary, Yuri and Cris, there is a match if each of them gets their own helmet. As there are 3 helmets, the total number of possible orders are 3! = 6. These are listed below

GYC

GCY

YGC

YCG

CGY

CYG

If the first helmet returned is G, then it's a match for Gary. If the second helmet returned is Y, then it's a match for Yuri, and if the third helmet returned is C, then it's a match for Cris. Using this reasoning, the number of correct matches denoted by the variable X is as shown in the below table

Thus, X={0,1,3}