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Rahul has a bag that contains strawberry chews, cherry chews, and lime chews. He performs an experiment. Rahul randomly removes a chew from the bag, records the result, and returns the chew to the bag. Rahul performs the experiment 76 times. The results are shown below:
A strawberry chew was selected 33 times.
A cherry chew was selected 8 times.
A lime chew was selected 35 times.
If the experiment is repeated 700 more times, about how many times would you expect Rahul to remove a lime chew from the bag? Round your answer to the nearest whole number.
Answer:

Rahul has a bag that contains strawberry chews, cherry chews, and lime chews. He performs an experiment. Rahul randomly removes a chew from the bag, records the result, and returns the chew to the bag. Rahul performs the experiment $76$ times. The results are shown below: $\newline$ A strawberry chew was selected $33$ times. $\newline$ A cherry chew was selected $8$ times. $\newline$ A lime chew was selected $35$ times. $\newline$ If the experiment is repeated $700$ more times, about how many times would you expect Rahul to remove a lime chew from the bag? Round your answer to the nearest whole number. $\newline$ Answer:

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Experiment design

Full solution

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

76

times. The results are shown below:

\newline

A strawberry chew was selected

33

times.

\newline

A cherry chew was selected

8

times.

\newline

A lime chew was selected

35

times.

\newline

If the experiment is repeated

700

more times, about how many times would you expect Rahul to remove a lime chew from the bag? Round your answer to the nearest whole number.

\newline

Answer:

Calculate Probability: First, we need to determine the probability of selecting a lime chew based on the initial $76$ trials. $\newline$ Probability of selecting a lime chew $=$ Number of times a lime chew was selected / Total number of trials $\newline$ Probability of selecting a lime chew $=$ $\frac{35}{76}$
Estimate Lime Chews: Next, we use the probability to estimate the number of times a lime chew would be selected if the experiment is repeated $700$ times. $\newline$ Expected number of lime chews = Probability of selecting a lime chew $\times$ Number of additional trials $\newline$ Expected number of lime chews = $(35 / 76) \times 700$
Calculate Expected Number: Now, we perform the calculation to find the expected number of lime chews. $\newline$ Expected number of lime chews = $(35 / 76) \times 700 \approx 322.37$ $\newline$ Since we need to round to the nearest whole number, we round $322.37$ to $322$ .
Conclusion: Finally, we conclude that if the experiment is repeated $700$ more times, we would expect Rahul to remove a lime chew from the bag approximately $322$ times.

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