As shown above, a classic deck of cards is made up of 52 cards, 26 are black, 26 are red. Each
color is split into two suits of 13 cards each (clubs and spades are black and hearts and
diamonds are red). Each suit is split into 13 individual cards (Ace, 2-10, Jack, Queen, and King).
A card is drawn randomly from a standard 52 -card deck. Find the probability of the given
event.
Write the probabilities as a simplified fraction.
(a) What is the probability of selecting a king or a queen?
(b) What is the probability of selecting a face card or a 10 ?
© What is the probability of selecting a spade or a heart?
(d) What is the probability of selecting a red card or a black card?
(

Question

UpStudy AI · Accepted Answer

**(a) Probability of selecting a king or a queen**

- A standard deck has 4 kings and 4 queens.
- Total favorable outcomes $$ = 4 + 4 = 8 $$.
- Total possible outcomes $$ = 52 $$.

$$
P(\text{king or queen}) = \frac{8}{52} = \frac{2}{13}
$$

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**(b) Probability of selecting a face card or a 10**

- Face cards are Jack, Queen, and King. Each suit has 3 face cards, so total face cards $$ = 3 \times 4 = 12 $$.
- There are 4 tens (one in each suit).
- Since no card is both a face card and a 10, the total favorable outcomes $$ = 12 + 4 = 16 $$.

$$
P(\text{face card or 10}) = \frac{16}{52} = \frac{4}{13}
$$

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**(c) Probability of selecting a spade or a heart**

- There are 13 spades and 13 hearts.
- Total favorable outcomes $$ = 13 + 13 = 26 $$ (note that spades and hearts are mutually exclusive suits).

$$
P(\text{spade or heart}) = \frac{26}{52} = \frac{1}{2}
$$

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**(d) Probability of selecting a red card or a black card**

- A red card is either a heart or a diamond ($$26$$ cards), and a black card is either a spade or a club ($$26$$ cards).
- Since every card is either red or black, the entire deck of 52 cards is favorable.

$$
P(\text{red or black}) = \frac{52}{52} = 1
$$
**(a) Probability of selecting a king or a queen:** $$ \frac{2}{13} $$ **(b) Probability of selecting a face card or a 10:** $$ \frac{4}{13} $$ **(c) Probability of selecting a spade or a heart:** $$ \frac{1}{2} $$ **(d) Probability of selecting a red card or a black card:** $$ 1 $$

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