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/** Probabilistic solver for a logic puzzle:
https://www.quantamagazine.org/perplexing-the-web-one-probability-puzzle-at-a-time-20240829/
"You have an urn filled with 100 balls, some red and some green. You can’t
see inside; all you know is that someone determined the number of red balls
by picking a number between zero and 100 from a hat. You reach into the urn
and pull out a ball. It’s red. If you now pull out a second ball, is it
more likely to be red or green (or are the two colors equally likely)?"
*/
trials = million
redFirstTrials = 0 // Number of trials in which the first ball drawn is red
redSecond = 0 // Number of trials in which the second ball drawn is red
for trial = 1 to trials
{
numRed = random[0, 100]
// Create an array of 100 balls which are either "red" or "green" with the
// number of red given by numRed
urn = new array[[100], {|x, data| x < data ? "red" : "green"}, numRed]
urn.shuffle[] // To eliminate any bias, shuffle using Fisher-Yates-Knuth
firstBall = urn.removeRandom[] // Draw a random first ball, removing it
if firstBall == "red"
{
// First ball was red
redFirstTrials = redFirstTrials + 1
secondBall = urn.removeRandom[] // Draw a random second ball
if secondBall == "red"
redSecond = redSecond + 1
}
}
// Calculate the ratio of second balls that are also red
println["The probability that the second ball is also red:"]
println[redSecond / redFirstTrials]
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This is a program written in the programming language Frink.
For more information, view the Frink
Documentation or see More Sample Frink Programs.
Alan Eliasen was born 20152 days, 19 hours, 27 minutes ago.