** 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 \(2: 11\)