SOLUTION: Is there any other way to solve this problem without actually listing out all of the outcomes? Thanks! <pre> Jacob uses the following procedure to write down a sequence of numb

Algebra ->  Probability-and-statistics -> SOLUTION: Is there any other way to solve this problem without actually listing out all of the outcomes? Thanks! <pre> Jacob uses the following procedure to write down a sequence of numb      Log On


   

Question 1195872: Is there any other way to solve this problem without actually listing out all of the outcomes? Thanks!



Jacob uses the following procedure to write down a sequence of numbers. First, he chooses the first term to be 6. To generate each succeeding term, he flips a fair coin. If it comes up heads, he doubles the previous term and subtracts 1. If it comes up tails, he takes half of the previous term and subtracts 1. What is the probability that the fourth term in Jacob's sequence is an integer?



https://artofproblemsolving.com/wiki/index.php/2008_AMC_10A_Problems/Problem_22 

Answer by greenestamps(13200) About Me  (Show Source): 

You can put this solution on YOUR website!
 


No; there is not really any other way.


Any "other" method of solving the problem will be equivalent to the method shown on the AOPS website.