Mark H. answered • 10/03/19

Tutoring in Math and Science at all levels

Each applicant has 5 choices, and they make these choices independently----thus the choices made be one are not related to the choices made by the other.

What is needed here is the probability that each applicant chooses the same 2 time slots. This can be found simply by noting that--once the first applicant's choices are made, the 2nd applicant sees 5 choices, including 2 "conflicts" which, if BOTH selected, means neither candidate will get an interview.

The odds of picking one conflict are 2/5. Once one slot is picked which is a conflict, then the remaining choices are 1 conflict out of 4 choices. Thus the odds of picking the second conflict is 1/4, and the combined odds are 2/5 * 1/4 = 1/10

This means the the probability of successfully scheduling the 2 interviews is 9/10 = 90%.