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.
For all cases, the probability one "at least one success" is the complement of "no successes" and so can easily be computed by subtracting the latter probability from one.
In the first case
1(5/6)^4≈.5177
In the second case
1(35/36)^24≈.4192
So it is more likely to get at least one six in four rolls than to get at least one doublesix in 24 rolls.
Increasing to 25 rolls does not change this
1(35/36)^25≈.5055
However, with 26 rolls this does the more likely outcome
1=(35/36)^26≈.5193

Posted by Jer
on 20160616 09:42:03 