The Bertrand Box paradox illustrates how intuition can fail when dealing with conditional probability. Imagine three sealed boxes: one contains two gold coins (GG), another contains two silver coins (SS), and the third contains one gold and one silver coin (GS). A box is chosen at random, then a coin is drawn at random from that box.
If the drawn coin happens to be gold, the question is: what is the probability that the remaining coin in the same box is also gold? Many people answer 1/2, but the correct answer is 2/3 because the GG box is twice as likely to produce a gold coin as the GS box.
Mathematically the problem is expressed by the conditional probability formula below. It compares the number of ways to draw a gold coin from a GG box (two ways per GG box) with the total number of ways to draw a gold coin from any box (two ways per GG box plus one way per GS box).
What is Bertrand's Box Paradox?
Why does intuition fail in this paradox?
How do I use this calculator?
What are the possible outcomes for the boxes?
Can this calculator be used for other probability problems?
What is the correct answer to the paradox?
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