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

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) (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 =.333...
So the probability that you didn't guess is  =.666...

The probability that you guessed correctly the first two times is  = .111...
So the probability that you didn't guess is  =.888...

The probability that you guessed correctly the first three times is  = .037037...
So the probability that you didn't guess is  =.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

RELATED QUESTIONS
An urn contains 4 red, 1 white, and 4 blue marbles. In how many ways can 3 red and 3... (answered by stanbon)

An urn contains 3 red, 1 white, and 4 blue marbles. In how many ways can 2 red and 3... (answered by sudhanshu_kmr)

An urn contains 7 red, 5 blue, and 3 white marbles. You draw three marbles randomly... (answered by mathmate)

We are gives two urns follows: Un A contains 6 red marbles, 2 white marbles and 3 blue... (answered by greenestamps)

An urn contains blue and purple marbles. The number of purple marbles is 3 more than... (answered by stanbon)

1/A batch contains 10 transistors of which three are defective. If three are chosen, in... (answered by jim_thompson5910)

26 In an urn I have 20 marbles: 2 red, 3 yellow, 4 blue, 5 green, and 6 black marbles.... (answered by greenestamps)

an urn contains 3 red marbles and 1 green marbles. if 2 marbles are selected at random... (answered by stanbon)

A jar has twice as many red marbles as white marbles and the ratio of blue marbles to... (answered by scott8148,stanbon)