SOLUTION: If I have an urn with an infinite number of marbles, 1/3 white, 1/3 blue and 1/3 red. If I claim clairvoyance and am blindfolded, how many marbles do I need to pick up and correctl

Algebra ->  Probability-and-statistics -> SOLUTION: If I have an urn with an infinite number of marbles, 1/3 white, 1/3 blue and 1/3 red. If I claim clairvoyance and am blindfolded, how many marbles do I need to pick up and correctl      Log On


   

Question 508401: If I have an urn with an infinite number of marbles, 1/3 white, 1/3 blue and 1/3 red. If I claim clairvoyance and am blindfolded, how many marbles do I need to pick up and correctly color code until it can be ascertained with a 95% probability that I am actually clairvoyant?
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
When the probability of my guessing correctly drops to 5% then there is
a 95% chance that I am clairvoyant. So we set the probability that I
guessed correctly N times in a row < .05
The probability that you guessed correctly the first time is 1%2F3=.333...
So the probability that you didn't guess is 2%2F3 =.666...

The probability that you guessed correctly the first two times is expr%281%2F3%29expr%281%2F3%29 = .111...
So the probability that you didn't guess is 1-.111 =.888...

The probability that you guessed correctly the first three times is expr%281%2F3%29expr%281%2F3%29%2Aexpr%281%2F3%29 = .037037...
So the probability that you didn't guess is 1-.037 =.962962...

So since the probability that you didn't guess is higher than .95 on the
third marble, then that is the answer: 3 marbles is all it takes to
get a probability greater than 95% that you couldn't do that 3 times in a row.

Edwin