Question

5. If one card is drawn from a deck, find the probability of getting these results.

a. A queen.

b. A club.

c. A queen of clubs.

d. A 3 or an 8.

e. A 6 or a spade.

f. A 6 and a spade.

g. A black king

h. A red card and a 7.

а

i. A diamond or a heart.

j. A black card.

Answer 1

There are 52 cards in a standard deck of cards

There are 4 of each card (4 Aces, 4 Kings, 4 Queens, etc.)

There are 4 suits (Clubs, Hearts, Diamonds, and Spades)

There are 13 cards in each suit (Clubs/Spades are black, Hearts/Diamonds are red) 

Each suit has 13 card values: 2-10, 3 “face cards” Jack, Queen, King (J, Q, K) and and Ace (A)

a.

$$P(Queen)=\dfrac{4}{52}=\dfrac{1}{13}$$

b.

$$P(Club)=\dfrac{13}{52}=\dfrac{1}{4}$$

c.

$$P(Queen\ or\ Club)=\dfrac{1}{13}+\dfrac{1}{4}-\dfrac{1}{52}=\dfrac{4}{13}$$

d.

$$P(3\ or\ 8)=\dfrac{1}{13}+\dfrac{1}{13}=\dfrac{2}{13}$$

e.

$$P(6\ or\ Club)=\dfrac{1}{13}+\dfrac{1}{4}-\dfrac{1}{52}=\dfrac{4}{13}$$

f.

$$P(6\ and\ Club)=\dfrac{1}{52}$$

g.

$$P(Black\ King)=\dfrac{2}{52}=\dfrac{1}{26}$$

h.

$$P(Red\ and\ 7)=\dfrac{2}{52}=\dfrac{1}{26}$$

i.

$$P(Diamond\ or\ Heart)=\dfrac{13}{52}+\dfrac{13}{52}=\dfrac{1}{2}$$

j.

$$P(Black)=\dfrac{26}{52}=\dfrac{1}{2}$$