3 Two cards are chosen at random without replacement from a

(3) Two cards are chosen at random without replacement from a deck of 52 cards. What is the probability that

(a) they are both aces?

(b) the second card is an ace if the first one is an ace?

Solution

there are 52 cards and two are choosen

a) both are aces = 52C2(1/13)^2*(12/13)^48 = 0.137  ( as we have to take two cards without putting back so the total card will reuce by 1 in 2nd chance also there are 4 aces in total which will reuce by one if 1st is also ace)

b) THE SECONG CARD ID ACES IF FIRST IS ALSO AN ACE = 3/51 = 1/17

AS TOTAL CARD WILL REDUCE BY 1 BEACUSE WE HAVE PICKED ONE

AND ALSO THE TOTAL ACE IS 4 AND IT WILL REDUCE BY 1 BECAUSE WE HAVE TAKEN OUT ACE AT 1ST CHANCE, HENCE ANSWER WILL BE 1/17