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You select a card at random. Without putting the first card back, you select another card at random. What is the probability of selecting a $3$ and then selecting a $4$ ? 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 select a card at random. Without putting the first card back, you select another card at random. What is the probability of selecting a

3

and then selecting a

4

? Write your answer as a fraction or whole number.

\newline

______

Probability of Selecting a $3$ : Assuming we are dealing with a standard deck of $52$ playing cards, there are $4$ cards of each rank. The probability of selecting a $3$ on the first draw is the number of $3$ s in the deck divided by the total number of cards. $\newline$ P(Selecting a $3$ ) = Number of $3$ s / Total number of cards $\newline$ = $\frac{4}{52}$ $\newline$ = $\frac{1}{13}$
Probability of Selecting a $4$ after a $3$ : After drawing a $3$ , there are now $51$ cards left in the deck. The probability of selecting a $4$ on the second draw, without replacing the first card, is the number of $4$ s remaining divided by the new total number of cards. $P(\text{Selecting a 4 after a 3}) = \frac{\text{Number of 4s}}{\text{Remaining number of cards}}$ $= \frac{4}{51}$
Combined Probability of Selecting a $3$ and then a $4$ : To find the combined probability of both events happening in sequence (selecting a $3$ and then a $4$ ), we multiply the probabilities of each individual event. $\newline$ P(Selecting a $3$ and then a $4$ ) = P(Selecting a $3$ ) $\times$ P(Selecting a $4$ after a $3$ ) $\newline$ = $(1 / 13) \times (4 / 51)$
Combined Probability of Selecting a $3$ and then a $4$ : To find the combined probability of both events happening in sequence (selecting a $3$ and then a $4$ ), we multiply the probabilities of each individual event. $\newline$ P(Selecting a $3$ and then a $4$ ) = P(Selecting a $3$ ) $\times$ P(Selecting a $4$ after a $3$ ) $\newline$ = $(1 / 13) \times (4 / 51)$ Now we perform the multiplication to find the combined probability. $\newline$ P(Selecting a $3$ and then a $4$ ) = $(1 / 13) \times (4 / 51)$ $\newline$ = $4 / (13 \times 51)$ $\newline$ = $4 / 663$

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\newline

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Question

X

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\newline

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\newline

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\newline

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\newline

Write your answer as a decimal rounded to the nearest thousandth.

\newline

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Complete the statement. Round your answer to the nearest thousandth.

\newline

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30\%

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