Question

If one card is drawn from a deck, find the probability of getting these results. a. An ace b. A diamond c. A 4 or a club d. A heart or a club e. A red card or a 7

Answer 1

A standard deck has 52 unique cards.

a.

From these 52 cards, 4 are aces, so the probability of picking an ace is:

$P=\frac{4}{52}=\frac{1}{13}$

b.

From the 52 cards, 13 are diamonds, so the probability of picking a diamond is:

$P=\frac{13}{52}=\frac{1}{4}$

c.

There are 4 numbers 4 and 13 clubs, and 1 card is both 4 and club, so the number of cards that are a 4 or a club is 4 + 13 - 1 = 16, so the probability is:

$P=\frac{16}{52}=\frac{4}{13}$

d.

There are 13 heart cards and 13 club cards, and no card is both at the same time, so the number of cards that are a heart or a club is 13 + 13 = 26, so the probability is:

$P=\frac{26}{52}=\frac{1}{2}$

e.

The number of red cards is 26 and the number of seven's is 4, and there are 2 sevens that are also red cards, so the number of red cards or 7 cards is 26 + 4 - 2 = 28, so the probability is:

$P=\frac{28}{52}=\frac{7}{13}$