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 probability as a decimal rounded to four decimal places if needed.
(a) a face card? (face)
(b) a diamond or a spade? (diamond or spade)
© a 2 or a 7 ? or 7
(d) an ace or a diamond? (ace or diamond)
(e) a face card or a diamond? face or diamond)
(f) a 7 or a red card? or red)
( 7 ,

Ask by Pritchard Huff. in the United States

Mar 31,2025

Question

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 probability as a decimal rounded to four decimal places if needed.
(a) a face card? (face)
(b) a diamond or a spade? (diamond or spade)
© a 2 or a 7 ? or 7
(d) an ace or a diamond? (ace or diamond)
(e) a face card or a diamond? face or diamond)
(f) a 7 or a red card? or red)
( 7 ,

Ask by Pritchard Huff. in the United States

Mar 31,2025

UpStudy AI · Accepted Answer

(a) There are 12 face cards (Jack, Queen, King in each of the 4 suits) in a 52‐card deck.
$$
P(\text{face}) = \frac{12}{52} = \frac{3}{13} \approx 0.2308.
$$

(b) There are 13 diamonds and 13 spades. Since a card cannot be both a diamond and a spade, their probabilities add.
$$
P(\text{diamond or spade}) = \frac{13 + 13}{52} = \frac{26}{52} = 0.5000.
$$

(c) There are 4 cards of 2 and 4 cards of 7.
$$
P(2 \text{ or } 7) = \frac{4 + 4}{52} = \frac{8}{52} = \frac{2}{13} \approx 0.1538.
$$

(d) There are 4 aces and 13 diamonds. However, the ace of diamonds is counted in both, so subtract 1.
$$
P(\text{ace or diamond}) = \frac{4 + 13 - 1}{52} = \frac{16}{52} = \frac{4}{13} \approx 0.3077.
$$

(e) There are 12 face cards and 13 diamonds. The overlapping cards (face cards that are diamonds) total 3 (Jack, Queen, King of diamonds). Thus,
$$
P(\text{face or diamond}) = \frac{12 + 13 - 3}{52} = \frac{22}{52} = \frac{11}{26} \approx 0.4231.
$$

(f) There are 4 sevens and 26 red cards. The red sevens (from hearts and diamonds) total 2. Therefore,
$$
P(7 \text{ or red}) = \frac{4 + 26 - 2}{52} = \frac{28}{52} = \frac{7}{13} \approx 0.5385.
$$
(a) $$ P(\text{face}) = 0.2308 $$ (b) $$ P(\text{diamond or spade}) = 0.5000 $$ (c) $$ P(2 \text{ or } 7) = 0.1538 $$ (d) $$ P(\text{ace or diamond}) = 0.3077 $$ (e) $$ P(\text{face or diamond}) = 0.4231 $$ (f) $$ P(7 \text{ or red}) = 0.5385 $$

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