SOLUTION: A designer is creating a store window display from 3 pairs of pants (black, brown, blue); 2 shirts (black and blue); and 3 pairs of shoes (black, brown, blue) that are available to

Algebra ->  Probability-and-statistics -> SOLUTION: A designer is creating a store window display from 3 pairs of pants (black, brown, blue); 2 shirts (black and blue); and 3 pairs of shoes (black, brown, blue) that are available to      Log On


   



Question 1112837: A designer is creating a store window display from 3 pairs of pants (black, brown, blue); 2 shirts (black and blue); and 3 pairs of shoes (black, brown, blue) that are available to choose from. What is the probability that the outfit consists entirely of the same color if the components are chosen randomly?
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


All black: %281%2F3%29%281%2F2%29%281%2F3%29+=+1%2F18
All brown: %281%2F3%29%280%2F2%29%281%2F3%29+=+0
All blue: %281%2F3%29%281%2F2%29%281%2F3%29+=+1%2F18

All the same color: 1%2F18%2B0%2B1%2F18%29+=+2%2F18+=+1%2F9
Answer: 1/9 probability that all are the same color.

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OR...

3*2*3=18 possible combinations total;
2 combinations with all the same color (black or blue);
probability that all are the same color: 2/18 = 1/9