your company is considering offering 400 employees the opportunity to transfer t

Question

your company is considering offering 400 employees the opportunity to transfer to its new headquarters in Ottawa and, as personnel manager, you decide that it would be fairest if the transfer offers are decided by means of a lottery. Assuming that your company currently employs 100 managers, 300 factory workers, and 600 miscellaneous staff, find the following probabilities, leaving the answers as formulas. A) all the managers will be offered the opportunity. B) you will be offered the opportunity.

Explanation / Answer

There are 1000 people in total :100 managers, 300 factory workers, and 600 miscellaneous staff

a. P(all the managers will be offered the opportunity) = 100C100 * 900C300 / 1000C400

It basically says pick all 100 managers from 100 managers available, and pick 300 from rest 900

b. P(you will be offered the opportunity. ) = 1C1*1000C399 / 1001C400

So, choose yourself to be employed in 1 way , and choose rest 399 from rest 1000 people avaiable. Denominator is choosing 400 people out of 1000+1(yourself) available.

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