Colored Chips Bin
A bin contains blue chips, red chips, green chips, and yellow chips. The probability of drawing a red chip, putting it back in the bin, then drawing a green chip can be written as , where and are positive, coprime integers. What is the value of ?
The answer is 368.
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1 solution
The total number of chips is 1 1 + 4 + 7 + 1 6 = 3 8 . The probability of drawing a red chip is 3 8 4 = 1 9 2 . Since the red chip is put back in the bin, the total number of chips stays the same. Thus the probability of then drawing a green chip is 3 8 7 .
Therefore, by the rule of product, the probability of drawing a red and then a green chip is 1 9 2 ⋅ 3 8 7 = 3 6 1 7 .
Hence a + b = 7 + 3 6 1 = 3 6 8 .