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Coin toss bijection

Source: AMC 10B 2021 #14

November 17, 2021
probabilityAMCAMC 10AMC 10 BAMC 12AMC 12 B

Problem Statement

Una rolls 66 standard 66-sided dice simultaneously and calculates the product of the 66{ } numbers obtained. What is the probability that the product is divisible by 4?4?
<spanclass=′latex−bold′>(A)</span> 34<spanclass=′latex−bold′>(B)</span> 5764<spanclass=′latex−bold′>(C)</span> 5964<spanclass=′latex−bold′>(D)</span> 187192<spanclass=′latex−bold′>(E)</span> 6364<span class='latex-bold'>(A)</span>\: \frac34\qquad<span class='latex-bold'>(B)</span> \: \frac{57}{64}\qquad<span class='latex-bold'>(C)</span> \: \frac{59}{64}\qquad<span class='latex-bold'>(D)</span> \: \frac{187}{192}\qquad<span class='latex-bold'>(E)</span> \: \frac{63}{64}
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