At a homeowners\' association meeting, a board member can vote yes, vote no, or

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 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 exactly two of the motions. (Type an integer or a simplified fraction.) (c) Determine the probability that a board member votes yes on at least one motion (Type an integer or a simplified fraction.)

Explanation / Answer

a) For each motion, board member has 3 options and there are 3 motions. Hence,

Number of points in sample space = 3*3*3 = 27

b) P(Yes on exactly two of the motions) = 3C2 * (1/3)2 (2/3) = 2/9

c) P(Yes on atleast one motion) = 1 - (2/3)3 = 19/27

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