Question

Committee Selection. Refer to the image below for each of the following events, list the outcomes that constitute the event, and describe the event in words.

a. (not A)

b. (B&D)

c. (B or C)

A committee consists of five executives, three women and two men. Their names are Maria (M), John (J), Susan (S), Will (W), and Holly (H). The committee needs to select a chairperson and a secretary. It decides to make the selection randomly by drawing straws. The person getting the longest straw will be appointed chairperson, and the one getting the shortest straw will be appointed secretary. The possible outcomes can be represented in the following manner.

Short answer

Part a. Event not A potential results are MS, SM, HM, MH, SH, HS, MJ, SJ, HJ, MW, SW, HW

In words not A happens when female is chosen as chairperson.

Part b. Event B & D potential results are HM, HS

In words B & D happens when Holly is chosen as chairperson and one of Maria or Susan as Secretary

Part c. Event B or C i.e. potential results are HM, HS, HJ, HW, MW, SW, JW

In words B or C happens when Holly is chosen as chairperson or Will as Secretary.

Step-by-step solution

Part  (a)   Step 1. Given information

The potential results to chose chairperson and secretary from Maria (M), John (J), Susan(S), Will (W) and Holly (H) are

MS, SM, HM, JM, WM

MH, SH, HS, JS, WS

MJ, SJ, HJ, JH, WH

MW, SW, HW, JW, WJ

A= event a male is chosen as chairperson

B= event Holly is chosen as chairperson

C= event Will is chosen as secretary

D= event only chosen are appointed

Part  (a)  Step 2. Utilized principle and Equation  

The probability of an event lie between 0 to 1 and both are applicable.

$Probabilityofaneventis:P\left(E\right)=\frac{No.ofdesiredoutcomes}{Totalno.ofoutcomes}$

Part  (a)   Step 3. Calculation

It is provided that there are five executive 3 females (Maria, Susan and Holly) and 2 males i.e. (John and Will). And two person are chosen at random first is chairperson and second is secretary.

Now,

A= where a male is chosen as chairperson

potential results are JM, WM, JS, WS, JH, WH, JW, WJ

B= where Holly is chosen as chairperson

potential results are HM, HS, HJ, HW

C= where Will is chosen as secretary

potential results are MW, SW, HW, JW

D= where only females are chosen

potential results are MS, SM, HM, MH, SH, HS

Now,

Event not A potential results are MS, SM, HM, MH, SH, HS, MJ, SJ, HJ, MW, SW, HW

In words not A happens when a female is appointed as chairperson.

Part  (b)  Step 1. Calculation 

It is provided that there are five executive 3 females (Maria, Susan and Holly) and 2 males i.e. (John and Will). And two person are chosen at random first is chairperson and second is secretary.

Now,

A= where a male is chosen as chairperson

potential results are JM, WM, JS, WS, JH, WH, JW, WJ

B= where Holly is chosen as chairperson

potential results are HM, HS, HJ, HW

C= where Will is chosen as secretary

potential results are MW, SW, HW, JW

D= where only females are chosen

potential results are MS, SM, HM, MH, SH, HS

Now,

Event B & D i.e. common of B & D potential results are HM, HS

In words B & D happens when Holly is chosen as chairperson and one of Maria or Susan as Secretary.

Part (c)  Step 1. Calculation 

It is provided that there are five executive 3 females (Maria, Susan and Holly) and 2 males i.e. (John and Will). And two person are chosen at random first is chairperson and second is secretary.

Now,

A= where a male is chosen as chairperson

potential results are JM, WM, JS, WS, JH, WH, JW, WJ

B= where Holly is chosen as chairperson

potential results are HM, HS, HJ, HW

C= where Will is chosen as secretary

potential results are MW, SW, HW, JW

D= where only females are chosen

potential results are MS, SM, HM, MH, SH, HS

Now,

Event B or C i.e. Total of B and C potential results are HM, HS, HJ, HW, MW, SW, JW

In words B or C happens when Holly is chosen as chairperson or Will as Secretary.