SOLUTION: A homeowner's association meeting, a board member can vote yes vote no or abstain from a motion. There are three motions on which dashboard member must vote. Determine the number o

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Question 1044884: A homeowner's association meeting, a board member can vote yes vote no or abstain from a motion. There are three motions on which dashboard member must vote. Determine the number of points in a sample space. Determine the probability that a board member votes yes on all of the motions. Determine the probability that a board member votes yes on at least one. (Simplify fractions)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Y = member votes yes
N = member votes no
A = member abstains

Sample Space
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

Those are all the possible outcomes. There are 27 items in the sample space above. There's only one case of YYY out of the 27 cases total. So the probability of voting all yes is 1/27.


There are 8 cases where Y doesn't show up at all. Those cases are
NNN
NNA
NAN
NAA
ANN
ANA
AAN
AAA

This means there are 27-8 = 19 cases where Y shows up at least once.

So the probability of voting at least one yes (Y) is 19/27


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Summary:

The answer to the problem "Determine the number of points in a sample space." is 27

The answer to the problem "Determine the probability that a board member votes yes on all of the motions." is the fraction 1/27

The answer to the problem "Determine the probability that a board member votes yes on at least one." is the fraction 19/27