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Restaurants often slip takeout menus under Tim's apartment door. So far, Tim has collected $5$ menus for Italian food and $10$ other menus. What is the experimental probability that the next menu slipped under Tim's door will be from an Italian restaurant? Simplify your answer and write it as a fraction or whole number. $\newline$ $P(\text{Italian}) = \_\_$

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Experimental probability

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Q. Restaurants often slip takeout menus under Tim's apartment door. So far, Tim has collected

5

menus for Italian food and

10

other menus. What is the experimental probability that the next menu slipped under Tim's door will be from an Italian restaurant? Simplify your answer and write it as a fraction or whole number.

\newline

P(\text{Italian}) = \_\_

Identify Total Number: Identify the total number of menus collected by Tim so far. $\newline$ Tim has collected $5$ menus for Italian food and $10$ other menus. Therefore, the total number of menus is: $\newline$ $5$ (Italian menus) + $10$ (other menus) = $15$ menus.
Determine Favorable Outcomes: Determine the number of favorable outcomes for the event of interest. The event of interest is receiving an Italian menu. The number of favorable outcomes is the number of Italian menus Tim has, which is $5$ .
Calculate Experimental Probability: Calculate the experimental probability of the event. $\newline$ The experimental probability $P$ of an event is given by the ratio of the number of favorable outcomes to the total number of outcomes. In this case, the probability that the next menu is Italian is: $\newline$ $P(\text{Italian}) = \frac{\text{Number of Italian menus}}{\text{Total number of menus}}$ $\newline$ $P(\text{Italian}) = \frac{5}{15}$
Simplify Fraction: Simplify the fraction to find the experimental probability. $\newline$ To simplify the fraction $\frac{5}{15}$ , we divide both the numerator and the denominator by their greatest common divisor, which is $5$ . $\newline$ $P(\text{Italian}) = \left(\frac{5 \div 5}{15 \div 5}\right)$ $\newline$ $P(\text{Italian}) = \frac{1}{3}$

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