At a homeowners association meeting a board member can vote

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 member must vote. Complete parts (a) through (c) below. (a) Determine the number of points in the sample space. (b) Determine the probability that a board member votes yes on all three of the motions. (c). Determine the probability that a board member votes yes on at least one motion.

Solution

a)

There are three motions and for each they have 3 options. Therefore total number of sample points = 3*3*3 = 27

b)

the probability that a board member votes yes on all three of the motions = 3/27 = 1/9

c)

yes on at least one motion: 1 -P(all abstain or all \"no\") = 1- 2/9 = 7/9