SOLUTION: Sam has 17 ties. He has 6 green, 3 blue and 8 red. If he selects two ties at random, what is the probability that both ties are different colors? Round your answer to two dec

Algebra ->  Probability-and-statistics -> SOLUTION: Sam has 17 ties. He has 6 green, 3 blue and 8 red. If he selects two ties at random, what is the probability that both ties are different colors? Round your answer to two dec      Log On


   

Question 533872: Sam has 17 ties. He has 6 green, 3 blue and 8 red. If he selects two ties at random, what is the probability that both ties are different colors? Round your answer to two decimal places.

Answer:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
I would first find the probability
that both ties are the same
Both green: +%286%2F17%29%2A%285%2F16%29+
Both blue: +%283%2F17%29%2A%282%2F16%29+
Both red: +%288%2F17%29%2A%287%2F16%29+
The ties are the same color if he has
( both green ) OR ( both blue ) OR ( both red )
When things are OR'd you add the probabilities

+%28+1+%2F+%28+17%2A16+%29+%29%2A%28++6%2A5+%2B+3%2A2+%2B+8%2A7+%29+
+%28+1%2F272+%29%2A%28+30+%2B+6+%2B+56+%29+
+92+%2F+272+=+23%2F68+
The probability that none of these happen is
+1+-+23%2F68+=+45%2F68+
That would be better than 50-50 odds
I would get a 2nd opinion on this. I'm in
kind of deep water with probabilities