When I swing at a nail, I drive it all the way in with probability 1/2. With probability 1/4, I hit it half-way in, and with 1/4 probability I miss it entirely. Hitting it half-way in twice will drive it all of the way in. I'm pretty sure that if I swing 4 times at a nail, I'll get it all the way in almost all the time. Let's see if I'm right.

How many sequences of 4 swings could leave the nail still not knocked all the way in?

Guest Nov 13, 2017

1+0 Answers


Let H = Halfway in

Let M = Miss


So......any one of these sequences would not leave the nail not knocked all the way in








So.....5 sequences


cool cool cool

CPhill  Nov 13, 2017

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