Odds of winning the Christmas Lottery

In the Sorteo Extraordinario de Navidad, 165 series of 100,000 tickets (from number 00000 to 99999) are currently in play, of which 13,334 are awarded prizes. Given that 15,304 prizes are awarded between the Gordo, the second, the third, the fourth, the fifth, the approximations to some of them, the "pedreas" and the reintegros, we have that in this draw there will be 25,251,600 winning tickets (that is, the product of the 15,304 prizes by the 1,650 tickets that each number has). Taking into account that in total 100,000 - 10 - 165 = 165,000,000,000 tickets are sold, we have that the probability that our ticket obtains some prize is the following one:

P(prize) = 25.251.600/165.000.000 = 0,15304 (15,30%)

Thus, for example, if we play a lottery ticket in the Christmas prize, the probability of winning the jackpot of 4,000,000 € ("el gordo") is 1 in 100,000 (1 divided by the numbers of a series because all series have the same prizes).

P(gordo) = 1/100.000 = 0,00001 (0,001%)