## Thursday, May 12, 2011

### No One Volunteered to Put an Apple on Their Head

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William is playing archery blindfolded. The first arrow he shoots, unfortunately misses the bulls eye. The second arrow misses the bulls eye by an even wider margin. William shoots his third and final arrow.

How likely is it William's third shot is also worse than his first shot?

1. You're not given the probability he hits it in the first place so you can't make a proper tree diagram. Generally speaking though, I'd say he would get better than his second shot since he would have learned which steps to take to correct his aim. Since you only have 2 options though 'better' or 'worse' or even 'same' if you want to be pedantic you could say the chance would be 1/2 or 1/3 but there's so many other factors involved.

2. Without feedback, William is probably trying to correct his line. In that case, he should be trying to hit either between the two shots or even further out. So my guess is that he is going to be at least as wide off as the first shot.

3. There were some other comments with interesting answers here, but then Blogger went belly-up from Wednesday to Friday, which removed those comments. Sorry about that.

The answer depends on how you interpret the situation, I guess. If William is getting no feedback on his shots, then his third shot is just as likely to be off target as his first, irregardless of how off his second shot was.

If he's getting some sort of feedback (I was implying he wasn't supposed to since he's blindfolded) then as some of you pointed out in the comments that were lost that the probabilities get a lot more complicated, if not impossible, to project.

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