Question

You are dealt two cards successively (without replacement) from a shuffled deck of 52 playing cards. Find the probability that the first card is a King and the second card is a Queen. Question 3 options: a) 13/102 b) 4/663 c) 1/663 d) 2/13

Answer 1

Given :-

There are 4 Kings in the 52 card deck:
K of Spades
K of Clubs
K of Diamonds
K of Hearts
There are 4 chances in 52 that I will be dealt
a King on the first card

i.e (4/52) = (1/13)

The important words is AND:
the first card is a king AND the second card is a queen.
When you want the probability of both events happening,
you multiply the probabilities.
After I have the 1st card, there are 51 cards left
There are 4 queens
Q of Spades
Q of Clubs
Q of Diamonds
Q of Hearts
There are 4 chances in 51 that I will be dealt a Queen on the second card

i.e. (4/51)

The probability of getting both the King and the Queen is:

( 1/13 ) * ( 4/51 ) = [ (1*4) / (13*51) ] = ( 4/663 )

## Answer :- Option "b" is correct.