Complete a-c

Question

at a homeowners association meeting , a board member can vote yes, vote no, or abstain on a motion. There are three motions on which each board membe must vote.

 

a) determine the number of points in the sample space 

 

b) determine the probability that a board member votes yes on exactly two of the motions

 

c) determine the probability that a board member votes yes on at least one motion

 

 

Answer 1

There are 3^3=27 outcomes

YYY

YYN

YYA

YNY

YNN

YNA

YAY

YAN

YAA

NYY

NYN

NYA

NNY

NNN

NNA

NAY

NAN

NAA

AYY

AYN

AYA

ANY

ANN

ANA

AAY

AAN

AAA

(b) 6/27 =2/9

The non-Yes can be either No or abstain, so that is two possibilities

the arrangement is 3!/(2!1!) = 6/2 = 3

2*3 = 6

so 6/27 = 2/9

(c) 19/27

Probability of at least one yes is the same as 1 minus probability of zero

that limits the sample space to 2^3 = 8 possible responses

AAA

AAN

ANA

ANN

NAA

NAN

NNA

NNN

therefore 1 - 8/27 = 19/27