You pick a card at random. 567 What is P(5)? Write your answer as a fraction or whole number. _____

Identify Total Number: Identify the total number of cards and the specific cards of interest. Total cards = 567 Cards with the number 5 = 5, 15, 25, ..., 565 We need to find how many numbers between 1 and 567 end in 5. Calculate Number of Cards: Calculate the number of cards that end in 5. The sequence starts at 5 and increases by 10 each time (5, 15, 25, ..., 565). Using the formula for the nth term of an arithmetic sequence, $ a_n = a_1 + (n-1) \cdot d $, where $ a_1 = 5 $ and $ d = 10 $. Set $ a_n = 565 $ and solve for n: 565 = 5 + (n-1) \cdot 10 560 = (n-1) \cdot 10 n - 1 = 56 n = 57 There are 57 cards that end in 5. Calculate Probability: Calculate the probability P(5). P(5) = Number of favorable outcomes / Total number of outcomes P(5) = 57 / 567 Simplify the fraction by dividing both numerator and denominator by their greatest common divisor, which is 3. P(5) = 19 / 189

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You pick a card at random. $\newline$ $567$ $\newline$ What is $P(5)$ ? $\newline$ Write your answer as a fraction or whole number. $\newline$ $\_\_\_\_\_$

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Grade 7

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Q. You pick a card at random.

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567

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What is

P(5)

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Write your answer as a fraction or whole number.

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\_\_\_\_\_

Identify Total Number: Identify the total number of cards and the specific cards of interest. $\newline$ Total cards = $567$ $\newline$ Cards with the number $5 = 5, 15, 25, \ldots, 565$ $\newline$ We need to find how many numbers between $1$ and $567$ end in $5$ .
Calculate Number of Cards: Calculate the number of cards that end in $5$ . $\newline$ The sequence starts at $5$ and increases by $10$ each time ( $5$ , $15$ , $25$ , ..., $565$ ). $\newline$ Using the formula for the nth term of an arithmetic sequence, $a_n = a_1 + (n-1) \cdot d$ , where $a_1 = 5$ and $d = 10$ . $\newline$ Set $a_n = 565$ and solve for n: $\newline$ $565$ = $5$ + (n $-1$ ) \cdot $10$ $\newline$ $560$ = (n $-1$ ) \cdot $10$ $\newline$ n - $1$ = $56$ $\newline$ n = $57$ $\newline$ There are $57$ cards that end in $5$ .
Calculate Probability: Calculate the probability $P(5)$ . $\newline$ $P(5) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$ $\newline$ $P(5) = \frac{57}{567}$ $\newline$ Simplify the fraction by dividing both numerator and denominator by their greatest common divisor, which is $3$ . $\newline$ $P(5) = \frac{19}{189}$