From a deck of 52 cards 2 cards are drawn at random but you

From a deck of 52 cards, 2 cards are drawn at random, but you do not replace the first card before the second. What is the probability that....

A. Both cards will be the jack of diamonds

B. Both cards will be jacks

C. Both cards will diamonds

D. The first card will be an ace and the second a kind

Solution

A)
P( Drawn 2 cards are jack of diamonds) = 0, as you will have only one jack of diamond in a pair of card. Cards are not replaced after the first drawn, the only left jack has picked in 1st draw and there is no another jack of diamond to pick. Thus, probability such occurence never be true
B)
P( both cards are jacks) = 4 C 2 / 52 C 2 = (4!/(4-2)! 2! ) / (52!/(52-2)! 2! ) = 0.00452
C)
P( both cards are Diamonds) = 13 C 2 / 52 C 2 = (13!/(13-2)! 2! ) / (52!/(52-2)! 2! ) = 0.0588
D)
P( first card will be an ace and the second a kind) = 4 C 1 * 4 C 1 / 52 C 2 = 0.01206