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You draw a single card from a standard 52 -card deck. Find
a)
P (Queen | black)

$1$ . You draw a single card from a standard $52$ -card deck. Find $\newline$ a) $\mathrm{P}$ (Queen | black)

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Probability of one event

Full solution

Q.

1

. You draw a single card from a standard

52

-card deck. Find

\newline

a)

\mathrm{P}

(Queen | black)

Determine Probability of Drawing: We need to determine the probability of drawing a Queen from the black cards in a standard deck. There are $2$ suits of black cards in a deck: spades and clubs. Each suit has one Queen.
Find Total Black Cards: First, let's find the total number of black cards in the deck. Since there are two black suits and each suit has $13$ cards, we have $2$ suits $\times 13$ cards/suit $= 26$ black cards.
Find Number of Black Queens: Now, we need to find the number of black Queens. As mentioned, there is one Queen in each black suit, so there are $2$ black Queens in total.
Calculate Probability: The probability of an event is given by the number of favorable outcomes divided by the total number of possible outcomes. In this case, the favorable outcomes are the black Queens, and the possible outcomes are all black cards.
Simplify Fraction: So, the probability of drawing a Queen given that the card is black $P(Queen | black)$ is $2$ (black Queens) / $26$ (total black cards).
Final Probability Calculation: Calculating this probability gives us $P(Queen | black) = \frac{2}{26}$ . This fraction can be simplified by dividing both the numerator and the denominator by $2$ .
Final Probability Calculation: Calculating this probability gives us $P(Queen | black) = \frac{2}{26}$ . This fraction can be simplified by dividing both the numerator and the denominator by $2$ .After simplifying, we get $P(Queen | black) = \frac{1}{13}$ .

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