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You pick a card at random. Without putting the first card back, you pick a second card at random. $\newline$ $456$ $\newline$ What is the probability of picking a $5$ and then picking a $6$ ? $\newline$ 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 pick a card at random. Without putting the first card back, you pick a second card at random.

\newline

456

\newline

What is the probability of picking a

5

and then picking a

6

?

\newline

Write your answer as a fraction or whole number.

\newline

\_\_\_\_

Calculate Probability of Picking $5$ : Step $1$ : Calculate the probability of picking a $5$ from a standard deck of $52$ cards. There are four $5$ s in a deck (one for each suit). $\newline$ Probability of first $5 = \frac{\text{Number of 5s}}{\text{Total number of cards}} = \frac{4}{52} = \frac{1}{13}.$
Calculate Probability of Picking $6$ : Step $2$ : Calculate the probability of picking a $6$ after a $5$ has been picked. Now, there are $51$ cards left and still four $6$ s. $\newline$ Probability of second $6$ = Number of $6$ s / Remaining number of cards = $\frac{4}{51}$ .
Multiply Probabilities for Overall Probability: Step $3$ : Multiply the probabilities from Step $1$ and Step $2$ to find the overall probability of this two-card sequence. $\newline$ Overall probability = $(\frac{1}{13}) \times (\frac{4}{51}) = \frac{4}{663}$ .

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\newline

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\newline

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\newline

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