What is the probability of one employee being selected for both alcohol & drug test in the same quarter?

Question

I was trying to do the probability numbers on this equation.

I know SWA employees around 9k pilots.

I figure they would have about the same flight attendants.

Then they have MX workers, ops agent, dispatchers all classified as safety sensitive.

My guess is the number of employees in the drug testing pool is somewhere around 25k. The total number of employees is 49k.

So if 25% of those employees must be drug tested every year. Spread out over each quarter of the year. That is a total of 6,250 employees divided into 4 quarters. 1,562 employees would be selected every quarter.

Then you must test 10% of the same 25k employees for alcohol. That is 2,500 more employees selected. Over 4 quarters that is 625 employees selected.

What is the probability of one employee being selected for both alcohol & drug test in the same quarter?

Answer 1

The probability of being selected for both tests will be:

p(drug test) * p(alcohol test)

 

Since it is 1/4 of 25% and of 10%, respectively, that gives us

 

(.25/4)*(.1/4)

=.0625*.025

=.0015625

Answer 2

Miles,

 

The number of employees involved doesn't actually matter.

And lets assume we are only dealing with employees who could be administered the tests...i.e. the 25k.

 

Lets assume the allotments are set at the beginning of the year and we wish to find the answer to the question based on the elapse of one year.

 

Being chosen for drug testing or alcohol testing are independent events if the employees are picked randomly.

So the probability of being chosen for both during the whole year is .25*.1=.025

 

Now if we have assigned the drug testing of this individual to a particular quarter, the probability that this quarter independently is picked for alcohol testing is 1/4=.25

 

So the chances you are looking for are .025*.25=.00625...less than 1 pct.

 

In the question I would change "one employee" to "a given or particular employee"

 

Now there are other ways to interpret this question..."of at least one"..."of only one" which are much harder

problems that do require the number of employees involved to solve.