Question

Show how to compute the conditional probability of a straight flush given that the first two cards you are dealt are the 9 and 10 of hearts.

Answer 1

Straight Flush -   all 5 cards of the same suit with consecutive denomination except for the royal flush                          
for clubs, possible combination are                               
{A,2,3,4,5},{2,3,4,5.6},{3,4,5,6,7},{4,5,6,7,8},{5,6,7,8,9},{6,7,8,9,10},{7,8,9,10,J},{8,9,10,J,Q},{9,10,J,Q,K}                              
so, there are 9 possible combination.                              
similarly for diamonds, heards and spade.                              
so, total 4*9 = 36 possible outcomes                              
                              

given that the first two cards you are dealt are the 9 and 10 of hearts, total combination of st flush = 4*4=16

so, required probability = 16/36 = 4/9