Probability poker

If the king of size is included, the situation is much more complicated. Therefore, the king of size is removed here. In other words, the question becomes, what is the probability of randomly drawing 1 8 cards from 52 cards that contain at least1bomb? (Pay attention to the word "at least". This includes two, three or four "bombs". )

Obviously, the card of 18 is drawn from 52 cards, and * * has the drawing method of C (5218) = 42671977361650.

To calculate all the possibilities of containing 1, 2, 3 and 4 "bombs", the "inclusion-exclusion principle" can be used. The expression is as follows:

C( 13， 1)*C(48， 14) - C( 13，2)*C(44， 10) + C( 13，3)*C(40，6) - C( 13，4)*C(36，2)

=6077727399666

Therefore, the probability of randomly drawing 18 cards from 52 cards (excluding the king of size), including at least one "bomb", is

6077727399666 / 4267 197736 1650 = 0. 14242900787457 1860 17。