2008 AMC 10A Problem 22
Problem 22 of 25HarderNumber TheoryCounting & Probability
Jacob uses the following procedure to write down a sequence of numbers. First he chooses the first term to be To generate each succeeding term, he flips a fair coin. If it comes up heads, he doubles the previous term and subtracts If it comes up tails, he takes half of the previous term and subtracts What is the probability that the fourth term in Jacob’s sequence is an integer?
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Solution
Starting from the second terms are (heads) and (tails).
Continuing the tree, the eight equally likely fourth terms are
Of these, are integers, so the probability is
Thus, the correct answer is D.