There are five faculty members in a certain academic departm

There are five faculty members in a certain academic department. These individuals have 3, 6, 7, 10 and 14 years of teaching experience. Two of these individuals are randomly selected to serve on a personnel review committee. What is the probability that the chosen representatives have a total of at least 15 years of teaching experience? Consider all possible committees.

Solution

consider the total number of outcomes.

(3,6)(3,7)(3,10)(3,14)(6,7)(6,10)(6,14)(7,10)(7,14),(10,14).

n=10

Out of these 6 are favorable to the event that total experience is >=15.

m=6

P=6/10=0.6