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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?

 Nov 13, 2017
 #1
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Let H = Halfway in

Let M = Miss

 

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

 

{M,M,M,M}

{H,M,M,M}

{M,H,M,M}

{M,M,H,M}

{M,M,M,H}

 

So.....5 sequences

 

cool cool cool

 Nov 13, 2017

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