SOLUTION: Help, help help, these kinds of problems confuse me. A 3judge panel is used to settle a dispute. Both sides agree that a majority decision will be upheld. If each judge will ren

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Question 36315This question is from textbook Algebra 1
: Help, help help, these kinds of problems confuse me. A 3judge panel is used to settle a dispute. Both sides agree that a majority decision will be upheld. If each judge will render a favorable decision based on the evidence presented 2/3 of the tiem, what is the probability that the correct side will win the dispute? I've read this over and I don't even know how to begin. thank You This question is from textbook Algebra 1

Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
You get a correct decision is 2 judges or three judges
decide based on the evidence.
P(2 of three judge based on evidence)= 3C2(2/3)^2(1/3)=3(4/27)=12/27
P(3 of three judge based on evidence)= 3C3(2/3)^3=1(8/27)=8/27
Since these outcomes are mutually exclusive you add the probabilities
to get P(right decision based on evidence)= 12/27 + 8/27= 20/27
Cheers,
Stan H.