Chevalier de Méré (who was more gambler than mathematician) originally thought that rolling a 6 in 4 throws of a die was equiprobable to rolling a pair of 6's in 24 throws of a pair of dice.
In real life he would win the first bet more than half the time, but lose the second bet more than half the time.
He never understood, why.
de Méré asked his mathematician friend, Blaise Pascal, to explain this problem, which he did.
Over 330 years later I offer this issue to you.
Please provide your answer:
a.intuitively, i.e. prior to solving.
b. Final answer based upon your reasoning.
Enjoy wearing BP’s shoes!
a) From a reasoning standpoint, the second problem is an extension of the first by demanding a six on the second die. Thus the increase in rolls from 4 (x 6) to 24. So by that reasoning, the two should be "equiprobable".
b) Math Solution
The probability of the first is [1 - (5/6)^4] = 0.51775
The probability of the second is [1 - (35/36)^24] = 0.4914
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Posted by hoodat
on 2023-01-01 18:07:52 |
Solution
