A card is drawn randomly from a standard 52-card deck. Find the probability of the given event. Write your answers as reduced fractions or whole numbers.

Question

(a) The card drawn is 9

(b) The card drawn is not 9

(c) The card drawn is a face card (Jack, Queen, or King)

(d) The card drawn is not a face card.

Answer 1

(a) Since there are four 9's, the probability of drawing a 9 is 4/52 = 1/13

(b) Since there are four 9's, then there are 48 cards that are NOT 9 so the probability of drawing a card that is not 9 is 48/52 = 12/13

(c) There are 3 face cards per suit and 4 suits making 12 total face cards so the probability of drawing a face card is 12/52 = 3/13

(d) There are 3 face cards per suit and 4 suits making 12 total face cards which means there are 40 cards that are NOT face cards so the probability of drawing a card that is not a face card is 40/52 = 10/13

Notice that the probability of something happening + the probability of it NOT happening always add to 1.