# arrow_back a. What is the probability the 7 of spades is drawn?

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A card is drawn from a standard deck of 52 cards.

a. What is the probability the 7 of spades is drawn?

b. What is the probability that a 7 is drawn?

c. What is the probability that a face card is drawn?

d. What is the probability that a heart is drawn?

e. What are the odds that a heart is drawn?

f. What are the odds that a king or queen is drawn?

a. What is the probability the 7 of spades is drawn?

Let $\mathrm{N}$ be the number of cards in a deck of cards.
Let $S$ be the number of "seven of spades" in the deck.
The probability of drawing the "seven of spades" is $S / N$
If there are 52 cards then $N=52$.
If there is 1 "seven of spades" in the deck then $S=1$.
Then the probability of drawing the "seven of spades" from a deck of cards is $1 / 52$ or $0.01923$ or $1.923 \%$

b. What is the probability that a 7 is drawn?

There are four 7s in a standard deck, and there are a total of 52 cards. So:

$P(7) = \dfrac{4}{52} =\dfrac{1}{13}$

c. What is the probability that a face card is drawn?

$P(Face_Card) = \dfrac{12}{52}=\dfrac{3}{13}$

d. What is the probability that a heart is drawn?

A standard deck contains an equal number of hearts, diamonds, clubs, and spades. So the probability of drawing a heart is:

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

e. What are the odds that a heart is drawn?

The odds in favor are expressed as [the number of favorable outcomes]:[the number of unfavorable outcomes] and then divide out any common factors.

In a 52 card deck there are 4 suits, so 52 divided by 4 is 13 -- hence there are 13 hearts. 52 minus 13 is 39, so there are 39 cards that are not hearts. So if drawing a heart is considered a favorable outcome, then there are 13 possible favorable outcomes, and there are 39 possible unfavorable outcomes. Hence, the odds in favor of drawing a heart are 13 to 39. But notice that both 13 and 39 are evenly divisible by 13, so reduced to lowest terms we have 1 to 3.

f. What are the odds that a king or queen is drawn?

8 kings and queens to 44 non-kings and non queens $=8: 44$ which reduces to $2: 11$

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