Compare probability of getting at least one "6" in four rolls of a single 6sided die with the
probability of at least one doublesix in 24 throws of two dice,
Will the preference change if the two dice are thrown 25 times instead of 24 ?
Traced to: The French nobleman and gambler Chevalier de Méré.
The probability of not getting a 6 in four rolls is (5/6)^4 = 625/1296 ~= .4822530864197532, making the probability of actually getting a 6 approximately .5177469135802468.
The probability of not getting a double six in 24 throws of two dice is (35/36)^24 ~= .508596123869094, making the probability of actually getting a double six approximately .491403876130906.
Given 25 throws, that latter probability becomes 1(35/36)^25 ~= .505531546238381, which is still not as high as the single six in four rolls of one die.
You would have to go to 26 times to exceed the singlesix probability: 1(35/36)^26 ~= .519266781065093.

Posted by Charlie
on 20160616 09:43:00 