Ram has a machine which he calls RanGen (Random-Number Generator). RanGen generates random numbers b/w 0 and 1.
Ram is playing a game: He uses RanGen twice and hence gets 2 numbers 'a' and 'b'. Then he shows only 'a' to you and asks the following question: 'Is 'a' larger than 'b'??'.
If you guess the answer correctly, Ram gives you 101 Rs. Otherwise he takes 101 Rs from you. Ram is willing to play this game for ever, everytime with a new 'a' and 'b'.
Develop a scheme for guessing which will 'probably' make you rich in the long run.
Note that Ram is very kind, and will let you borrow RanGen for some time if you want.
err.. a quite basic guess.. i'll say yes if a is more than .5, otherwise no.. what say?
ReplyDeleteit won't 'probably' make you rich. the required strategy is such that "the probability that you guess correctly is greater than .5".
ReplyDeletealso, this question does not require knowledge of probability.
the correct answer is quite intuitive:
ReplyDelete'use RanGen again to get another number 'c'. if c>a then say "no, a is not greater than b", else say "yes, a is greater than b".'
Nice
ReplyDelete