Question

A club can select one member to attend a conference. All of the club officers want to attend. There are a total of four ​officers, and their designated positions within the club are President​ (P), Vice dash President (Upper V )comma Secretary (Upper S )comma nbspand Treasurer (Upper T ). For a simple random sample of one of the four officers who can attend the​ conference:

a. Show all the possible samples.
b. What is the chance that a particular sample of size 1 will be​ drawn?

Answer 1

0.25

Explanation:

Given that a club can select one member to attend a conference. All of the club officers want to attend. There are a total of four ​officers, and their designated positions within the club are President​ (P), Vice dash President (Upper V )comma Secretary (Upper S )comma nbspand Treasurer (Upper T ).

Sample space would be

a){ {P}, {V}, {S} {T}} is the sample space with notations standing for as given in the question

b) Each sample is equally likely. Hence we have equal chances for selecting any one out of the four.

If probability of selecting a particular sample of size I is p, the by total probability axiom we have

`4p =1\\p =0.25`