Acommittee of three people is selected at random from a set consisting of six teachers, five parents of students, and seven alumni. a. what is the probability of the event that the committee consists of all teachers? b. what is the probability of the event that the committee has no teachers?

0.0245 and 0.2696

Step-by-step explanation:

Given that there are six teachers, five parents of students, and seven alumni.

A committee of three people is selected at random from the above set

Without any condition, we see that total number of selecting three persons from these 18 persons is

a) the committee consists of all teachers

No of ways of selecting all teachers from 6 teachers =

Probability of the event that the committee consists of all teachers

=

b)  the committee has no teachers

This is equivalent to selecting 3 persons from 12 non teachers

= ways

the probability of the event that the committee has no teachers=

5x+2x=49

7x=49

x=7. 35 apples