45-733 PROBABILITY AND STATISTICS I


We Randomly chose 2 Denominations From 13; That is: 

                æ13ö
                ç  ÷
                è 2ø
So we have two piles of cards (4 cards each):


Let "a" and "b" stand for the denominations we randomly picked. We now have to account for the possibilities: aaabb and aabbb. To do this we have to choose one of the two to be the triple. There are 

                æ2ö
                ç ÷
                è1ø
Ways of doing this so we have one stack from which we will choose 3 cards


and one stack from which we will choose 2 cards.


Putting this all together:

                        æ13öæ2öæ4öæ4ö
                        ç  ÷ç ÷ç ÷ç ÷
                        è 2øè1øè3øè2ø
                 P(E) = ------------
                            æ52ö
                            ç  ÷
                            è 5ø