Problem:
A box contains shiny pennies and dull pennies. One by one, pennies are drawn at random from the box and not replaced. If the probability is that it will take more than four draws until the third shiny penny appears and is in lowest terms, then
Answer Choices:
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Solution:
Compute the probability that it takes or fewer draws to obtain the third shiny penny and subtract this from . Since there are are ways to select the shiny pennies in the first draws and ways to select them in all, the probability that the shiny pennies are drawn among the first is . Thus the requested probability is , whose numerator and denominator sum to .
Note. We could also have computed the first probability by considering the first coins drawn. There are ways to select the first coins and ways to select the shiny coins and one of the dull ones. Thus, the probability that the shiny pennies are among the first is .