Question

Your company is considering offering 500 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, 200 factory workers, and 400 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.

Answer 1

a)

`(^(500)C_(400))/(^(700)C_(500))`

b)

`(^(699)C_(499))/(^(700)C_(500))`

Explanation:

Given

The total number of opportunities to employees for transfer = 500

Company currently has 100 managers, 200 factory workers, and 400 miscellaneous staff

a) All the managers will be offered the opportunity

`(^(500)C_(400))/(^(700)C_(500))`

b) You will be offered the opportunity

`(^(699)C_(499))/(^(700)C_(500))`