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You grab a card at random. Without putting the first card back, you grab a second card at random. $\newline$ What is the probability of grabbing a Queen and then grabbing a King? $\newline$ Write your answer as a fraction or whole number. $\newline$ ______

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Probability of independent and dependent events

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Q. You grab a card at random. Without putting the first card back, you grab a second card at random.

\newline

What is the probability of grabbing a Queen and then grabbing a King?

\newline

Write your answer as a fraction or whole number.

\newline

______

Determine total number of cards: Determine the total number of cards in a standard deck and the number of Queens and Kings. $\newline$ A standard deck of cards has $52$ cards, with $4$ Queens and $4$ Kings.
Calculate probability of grabbing a Queen first: Calculate the probability of grabbing a Queen first. $\newline$ The probability of grabbing a Queen first is the number of Queens divided by the total number of cards. $\newline$ $P(\text{Grabbing a Queen}) = \frac{\text{Number of Queens}}{\text{Total number of cards}} = \frac{4}{52}$
Calculate probability of grabbing a King second without replacement: Calculate the probability of grabbing a King second without replacement. $\newline$ After grabbing a Queen, there are $51$ cards left and still $4$ Kings. $\newline$ $P(\text{Grabbing a King second}) = \frac{\text{Number of Kings}}{\text{Remaining number of cards}} = \frac{4}{51}$
Calculate combined probability of both events happening in sequence: Calculate the combined probability of both events happening in sequence. $\newline$ The combined probability is the product of the probabilities of each individual event. $\newline$ $P(\text{Grabbing a Queen and then a King}) = P(\text{Grabbing a Queen}) \times P(\text{Grabbing a King second}) = \left(\frac{4}{52}\right) \times \left(\frac{4}{51}\right)$
Simplify the fraction: Simplify the fraction. $\newline$ $P(\text{Grabbing a Queen and then a King}) = \frac{4}{52} \times \frac{4}{51} = \frac{1}{13} \times \frac{4}{51} = \frac{4}{13 \times 51} = \frac{4}{663}$

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