probability and statistics

Question

3 cards are drawn randomly from a deck of 52 cards. What is the probability that at least one is a heart and one is a king?

Answer 1

There are three suits other than hearts, and in each one, there are 12 cards that are not the king. Thus there are 36 cards that are neither a king nor a heart.

 

The complement is the event of choosing 3 of those 36 cards.

 

Thus:

 

P(1 + Hearts and 1+ Kings)

 

= 1 - P(No hearts and no kings)

 

= 1 - C(36,3)/C(52,3)

 

= 1 - [(36·35·34/3!)/(52·51·50/3!)]

 

= 1 - 21/65

 

= 44/65