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Two cards are drawn one by one without replacement from well shuffled pack of 52 cards. Find the probability distribution of the number of aces.

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A total number of possible ways of selecting two cards from the well-shuffled deck of 52 cards is C(52, 2) = 1326 ways.

Now we have to create a probability distribution of the number of aces. We know that there are 4 aces in the pack of 52 cards. Now, we will enumerate the different situations of the drawing of a number of aces. 

(i) A situation when we assume the draw of no any ace. Then, two cards will be drawn from the remaining 48 cards. Hence the probability of drawing two cards where no any ace become:

                      P(aces =0) = C(4,0)* C(48,2)/ C(52,2).

                                        = 188/221.

(ii) A situation when there is 1 ace and 1 another card from the remaining cards. The probability becomes: 

                      P (aces=1) = C(4,1)* C(48,1)/ C(52,2).

                                        = 32/221.

(iii) When both the drawn cards are aces. Then the probability becomes:

                     P (aces =2) = C(4,2)* C(48,0)/ C(52,2).


Now the probability distribution of the number of aces can be given in the table as given below:

Number of aces 0 1 2
P(Number of aces) 188/121 32/221 1/221


answered Jan 16 by dhimanmanish2060


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answered Jan 17 by mahawarravi036

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