SB 7.14 - probability

Question

14. Find the probability of drawing a heart or a face card from a standard deck of cards.

 

a) 25/52

b) 6/26

c) 1/4

d) 11/26

Answer 1

A standard deck has 52 cards.

 

Of these cards, 13/52 are hearts

 

Of the total cards in the deck, there are 12/52 face cards (16/52 if you include aces).

 

Of the face cards in the deck, 3/52 (4/52 with aces) are hearts.

 

If we add the total face cards with all of the hearts and subtract the intersection, we get 13/52 + 12/52 - 3/52 = 22/52 (13/52 + 16/52 - 4/52 = 25/52 including aces) cards that are either hearts or a face (or both).

 

This gives a probability of .4231 (.4808 with aces) that a randomly selected card from a standard deck will be a face or a heart.