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reinout-g

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 #37
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+3
Melody:
Quote:

Hard one :

You and your best friend have been arrested for several white collar crimes. (Or something else which is more classy than stealing a candy bar)
Your attorney has told you the police has only got enough evidence to put you and your friend behind bars for 3 years.
However, the both of you are given the option to confess. If both of you confess you will both serve 10 years,
if one of you confesses and the other does not, the one who did not confess will serve 20 years.
Obviously, if you both remain silent you will both serve 3 years.
You are not allowed to have any communication with your friend.
Suppose your main priority is to keep yourself out of jail, and your secondary priority is to keep your partner out of jail.
You have decided that you find it twice as important to keep yourself out of jail as you find it important to keep your partner out of jail.
(So for example, in your opinion him serving 10 years is equal to you serving 5).
You estimate the chance of your partner confessing p.
At what value of p will you choose to confess and at what value will you keep silent?



Maybe it doesn't make any difference to the question BUT If one confesses and the other doesn't then the non confessor gets 20yrs. HOW many years will the confessor get?



The confessor will get 0 years, but remember you do care about your friend. You want to keep yourself out of jail twice as much as you want to keep your partner out of jail. Therefore, you'd rather serve 4 years than have your friend serve 10 years (since 2*4 = 8 < 10), but you'd be indifferent between you serving 4 years and him serving 8. (Yes this puzzle does require some calculation)



edit: I just made an edit to the original question, I changed 'at which value of p' to 'for which values of p'. Sorry if I might have put you on the wrong foot
Apr 9, 2014
 #35
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+8
Melody:

Easier one:

Quote:

Ben the hiker wants to spend the night on top of a mountain. He hikes all day long towards the top and camps there overnight. The following day he is taking the same path down towards the bottom when he suddenly looks at his watch en notices that he is at the very same spot at the very same time of the day as the day before on his way up. 'What a coïncidence!' he exclaims!
Give an estimate of the probabilty that a hiker will be at exactly the same spot on the mountain at the same time of the day on his return trip as he was the previous day's hike up the mountain and explain why.


I think that the probability is 1. That means it has to happen.
This is why.
Ben's friend Sven is doing the same hike at exactly the same pace today, from the bottom to the top of the mountain that Ben did yesterday. Ben is on his way down. Somewhere Ben and Sven must pass each other. Obviously it will be the same time for each of them.
Although, Ben might have forgotten to set his watch back to mark the end daylight saving time. (Daylight savings finished on Sunday night in Sydney.) This could cause a problem.
No really, I think that the probablility is one - unless one of them falls and brakes his legs and has to get air lifted out. - then their paths may not cross.



You're right, assuming that all events like a dinosaur eating Ben are very close to 0, the probability of this happening is very close to 1. Did you think about the hard one yet?
Apr 8, 2014