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$Jonathan has a bag that contains pineapple chews, cherry chews, and watermelon chews. He performs an experiment. Jonathan randomly removes a chew from the bag, records the result, and returns the chew to the bag. Jonathan performs the experiment 22 times. The results are shown below: A pineapple chew was selected 5 times. A cherry chew was selected 13 times. A watermelon chew was selected 4 times. Based on these results, express the probability that the next chew Jonathan removes from the bag will be cherry or watermelon as a fraction in simplest form. Answer:$

Jonathan has a bag that contains pineapple chews, cherry chews, and watermelon chews. He performs an experiment. Jonathan randomly removes a chew from the bag, records the result, and returns the chew to the bag. Jonathan performs the experiment $22$ times. The results are shown below: $\newline$ A pineapple chew was selected $5$ times. $\newline$ A cherry chew was selected $13$ times. $\newline$ A watermelon chew was selected $4$ times. $\newline$ Based on these results, express the probability that the next chew Jonathan removes from the bag will be cherry or watermelon as a fraction in simplest form. $\newline$ Answer:

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Experiment design

Full solution

Q. Jonathan has a bag that contains pineapple chews, cherry chews, and watermelon chews. He performs an experiment. Jonathan randomly removes a chew from the bag, records the result, and returns the chew to the bag. Jonathan performs the experiment

22

times. The results are shown below:

\newline

A pineapple chew was selected

5

times.

\newline

A cherry chew was selected

13

times.

\newline

A watermelon chew was selected

4

times.

\newline

Based on these results, express the probability that the next chew Jonathan removes from the bag will be cherry or watermelon as a fraction in simplest form.

\newline

Answer:

Calculate Total Selections: Determine the total number of times a cherry or watermelon chew was selected. Cherry chews were selected $13$ times. Watermelon chews were selected $4$ times. Total for cherry or watermelon = $13$ (cherry) + $4$ (watermelon) Total for cherry or watermelon = $17$
Determine Experiments Conducted: Determine the total number of experiments conducted. Jonathan performed the experiment $22$ times.
Calculate Probability: Calculate the probability of selecting a cherry or watermelon chew. $\newline$ Probability = Number of favorable outcomes / Total number of experiments $\newline$ Probability (cherry or watermelon) = $\frac{17}{22}$
Simplify Fraction: Simplify the fraction to its simplest form. $17$ and $22$ have no common factors other than $1$ , so the fraction is already in its simplest form. Probability (cherry or watermelon) = $\frac{17}{22}$

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