Puzzle:
If you choose an answer to this puzzle at random, what is the probability of a correct guess?
a) 25%
b) 50%
c) 60%
d) 25%
1. Explain why the above puzzle is a paradox.
2. By introducing a single decimal point in one of the choices - can you convert this paradox into a solvable problem?
I'm thinking it is not a paradox after all.
in general, let's say there are n available choices for an answer, namely x(1),x(2),...,x(n)
now assume the true probability of guessing the correct answer is
0<=p<=1
now say that there are m>=0 occurrences of p among x(1),x(2),...,x(n)
the the probability of getting the right answer is m/n.
Now to avoid a paradox we require m/n=p
for for us n=4
x(1)=0.25,x(2)=0.50,x(3)=0.6,x(4)=0.25
now if p=0.25 then m=0.25*4=1 but m is actually 2 so p!=0.25
similarly for p=0.5 or p=0.6 we get a contradiction
thus p must not belong to any of the available answers, thus m=0
which gives p=0/n=0
thus there is a 0% chance of getting guessing the correct answer.
Of course this is all assuming that there doesn't have to be a right answer (which technically is not stated in the problem)
If, however, we require at least 1 correct choice, then changing either of the 25% values with a decimal point (e.g 2.5%) would result in p=25%
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Posted by Daniel
on 2015-04-06 10:58:03 |
answer...maybe
