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Zachary has a bag that contains strawberry chews, cherry chews, and peach chews. He performs an experiment. Zachary randomly removes a chew from the bag, records the result, and returns the chew to the bag. Zachary performs the experiment 66 times. The results are shown below:
A strawberry chew was selected 61 times.
A cherry chew was selected 3 times.
A peach chew was selected 2 times.
If the experiment is repeated 200 more times, about how many times would you expect Zachary to remove a peach chew from the bag? Round your answer to the nearest whole number.
Answer:

Zachary has a bag that contains strawberry chews, cherry chews, and peach chews. He performs an experiment. Zachary randomly removes a chew from the bag, records the result, and returns the chew to the bag. Zachary performs the experiment $66$ times. The results are shown below: $\newline$ A strawberry chew was selected $61$ times. $\newline$ A cherry chew was selected $3$ times. $\newline$ A peach chew was selected $2$ times. $\newline$ If the experiment is repeated $200$ more times, about how many times would you expect Zachary to remove a peach chew from the bag? Round your answer to the nearest whole number. $\newline$ Answer:

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Find probabilities using combinations and permutations

Full solution

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

66

times. The results are shown below:

\newline

A strawberry chew was selected

61

times.

\newline

A cherry chew was selected

3

times.

\newline

A peach chew was selected

2

times.

\newline

If the experiment is repeated

200

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

\newline

Answer:

Determine total number of experiments: Determine the total number of experiments conducted initially. Zachary performed the experiment $66$ times.
Determine peach chew selections: Determine the number of times a peach chew was selected. A peach chew was selected $2$ times out of the $66$ experiments.
Calculate experimental probability: Calculate the experimental probability of selecting a peach chew. Experimental probability of selecting a peach chew $= \frac{\text{Number of times a peach chew was selected}}{\text{Total number of experiments}} = \frac{2}{66}$
Simplify the probability: Simplify the probability. $\newline$ Experimental probability of selecting a peach chew = $\frac{2}{66}$ $\newline$ = $\frac{1}{33}$
Predict outcome of additional experiments: Use the experimental probability to predict the outcome of $200$ additional experiments. $\newline$ Expected number of times a peach chew will be selected = Probability of selecting a peach chew $\times$ Number of additional experiments $\newline$ $= \left(\frac{1}{33}\right) \times 200$
Perform calculation for expected selections: Perform the calculation to find the expected number of times a peach chew will be selected. $\newline$ Expected number of times a peach chew will be selected $\approx (1 / 33) \times 200$ $\newline$ $\approx 6.0606$
Round expected selections: Round the result to the nearest whole number. $\newline$ Expected number of times a peach chew will be selected $\approx 6$ (rounded to the nearest whole number)

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