Cavalier De Merè was a French nobleman who had a hobby: gambling. A day he wondered if it was more likely to get a 6, throwing a dice 4 times or to get double 6, throwing two dice 24 times.

He thought that it was irrelevant in both cases, but when he played the second combination he usually… Cavalier De Merè asked the question to one of his friends, Blaise Pascal. Pascal was a math genius of that time. Pascal created a modern Theory of Probability with another scientist.

This Theory states that the solution of the problem is in the definition of Complementary Events: two events, A and B, are called complementary if either A or B is certainly verified and it’s impossible for both to be verified. In that case we have: P(A)+P(B)=1

The event A consists in getting at least one 6 in 4 throws of a single dice, while the event B consists in getting a number that isn't a 6, in 4 throws of a single dice. P (B) = = 5 / 6 * 5 / 6 * 5 / 6 * 5 / 6 = = 625/1296 = = P (A) = 1 – = = 52%

The event A consists in getting at least one 12 in 24 throws of a double dice, while the event B consists in getting a number between 2 and 11 in 24 throws of a double dice. P (B) = (35 / 36)^24 =0,51P (A) = 1 – 0.51 = 0.49 = 49%

Getting 6 on your dice throwing it 4 times is more probably than......getting double 6 throwing two dice 24 times.