Question

You draw one card at random from a standard deck of 52 playing cards. Find the probability that (a) the card is an even-numbered card, (b) the card is a heart or a diamond, and (c) the card is a nine or a face card.?

Answer 1

Answer:

$P(even )=\frac{20}{52} =\frac{5}{13}$

$P(heart or diamond)=\frac{13}{52} +\frac{13}{52} =\frac{1}{2}$

$P(nine or face card)=\frac{4}{52} +\frac{12}{52} =\frac{4}{13}$

Step-by-step explanation:

You draw one card at random from a standard deck of 52 playing cards

Total cards = 52

5 even numbers in each suit. 4 times 5 = 20 even number cards

$P(even )=\frac{20}{52} =\frac{5}{13}$

(b) the card is a heart or a diamond

there are 13 heart and 13 diamonds

$P(heart or diamond)=\frac{13}{52} +\frac{13}{52} =\frac{1}{2}$

(c) the card is a nine or a face card

There are 4 nine and 12 face cards

$P(nine or face card)=\frac{4}{52} +\frac{12}{52} =\frac{4}{13}$