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Taub has a bag that contains orange chews, apple chews, and lime chews. She performs an experiment. Taub randomly removes a chew from the bag, records the result, and returns the chew to the bag. Taub performs the experiment 69 times. The results are shown below:
A orange chew was selected 57 times.
A apple chew was selected 8 times.
A lime chew was selected 4 times.
If the experiment is repeated 2000 more times, about how many times would you expect Taub to remove a apple chew from the bag? Round your answer to the nearest whole number.
Answer:

Taub has a bag that contains orange chews, apple chews, and lime chews. She performs an experiment. Taub randomly removes a chew from the bag, records the result, and returns the chew to the bag. Taub performs the experiment $69$ times. The results are shown below: $\newline$ A orange chew was selected $57$ times. $\newline$ A apple chew was selected $8$ times. $\newline$ A lime chew was selected $4$ times. $\newline$ If the experiment is repeated $2000$ more times, about how many times would you expect Taub to remove a apple chew from the bag? Round your answer to the nearest whole number. $\newline$ Answer:

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Experiment design

Full solution

Q. Taub has a bag that contains orange chews, apple chews, and lime chews. She performs an experiment. Taub randomly removes a chew from the bag, records the result, and returns the chew to the bag. Taub performs the experiment

69

times. The results are shown below:

\newline

A orange chew was selected

57

times.

\newline

A apple chew was selected

8

times.

\newline

A lime chew was selected

4

times.

\newline

If the experiment is repeated

2000

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

\newline

Answer:

Calculate Probability: Determine the probability of selecting an apple chew based on the initial experiment. $\newline$ Taub selected an apple chew $8$ times out of $69$ total selections. $\newline$ Probability of selecting an apple chew $=$ Number of apple chews selected $/$ Total number of selections $\newline$ Probability of selecting an apple chew $= \frac{8}{69}$
Estimate Selections in $2000$ Experiments: Use the probability to estimate the number of times an apple chew would be selected in $2000$ additional experiments. $\newline$ Expected number of times an apple chew is selected = Probability of selecting an apple chew $\times$ Number of additional experiments $\newline$ Expected number of times an apple chew is selected = $(8 / 69) \times 2000$
Calculate Expected Selections: Calculate the expected number of times an apple chew is selected. $\newline$ Expected number of times an apple chew is selected = $(8 / 69) \times 2000$ $\newline$ Expected number of times an apple chew is selected $\approx (0.11594202898550725) \times 2000$ $\newline$ Expected number of times an apple chew is selected $\approx 231.8840579710145$
Round to Nearest Whole Number: Round the result to the nearest whole number, as the question asks for an estimate. $\newline$ Expected number of times an apple chew is selected $\approx 232$ (rounded to the nearest whole number)

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