Answer to Question #259755 in Discrete Mathematics for rtf

Question

When drawing one card out of a deck of 52 playing cards, what is the probability of getting heart or a face card? There are 13 hearts and a total of 12 face cards (3 of each suit: spades, hearts, diamonds and clubs), but only 3 face cards of hearts.

Answer 1

There are 52 cards in a deck.

Each card can be categorized into 4 suits constituting 13 cards each.

Face Cards

They are Kings, Queens, and Jacks in all 4 suits.

$$P(heart\ or\ face)=\dfrac{13+4(3)-3}{52}=\dfrac{21}{52}$$