The members of a board of directors have the following roles: president (P), vice president (V), secretary (S), treasury (T), and fundraiser (F). Consider these board members to be a population of Interest. The possible samples (without replacement)of size two that can be obtained from these Five board members are as follows. $$\mathrm { P } , \mathrm { V } \text { P,S P,T P,F V,S V,T V,F S,T S,F T,F }$$
If a simple random sampling method is used to obtain a sample of two of the board members, what are the chances of selecting the secretary and the treasurer?
A)$\frac { 1 } { 20 }$
B) $\frac { 1 } { 10 }$
C) $\frac { 1 } { 5 }$
D) $\frac { 2 } { 5 }$

Question

The members of a board of directors have the following roles: president (P), vice president (V), secretary (S), treasury (T), and fundraiser (F). Consider these board members to be a population of Interest. The possible samples (without replacement)of size two that can be obtained from these Five board members are as follows. $$\mathrm { P } , \mathrm { V } \text { P,S P,T P,F V,S V,T V,F S,T S,F T,F }$$
If a simple random sampling method is used to obtain a sample of two of the board members, what are the chances of selecting the secretary and the treasurer?  
A)$\frac { 1 } { 20 }$
B) $\frac { 1 } { 10 }$
C) $\frac { 1 } { 5 }$
D) $\frac { 2 } { 5 }$

Quizplus · Accepted Answer

The total number of possible samples of size two from five members is 10 (as listed). Only one of these pairs is the secretary and the treasurer (S,T), so the probability is 1 out of 10, or $\frac{1}{10}$.

The Members of a Board of Directors Have the Following P,V P,S P,T P,F V,S V,T V,F S,T S,F T,F \mathrm { P } , \mathrm { V } \text { P,S P,T P,F V,S V,T V,F S,T S,F T,F }P,V P,S P,T P,F V,S V,T V,F S,T S,F T,F

The Members of a Board of Directors Have the Following $\mathrm { P } , \mathrm { V } \text { P,S P,T P,F V,S V,T V,F S,T S,F T,F }$