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Elizabeth has a bag that contains orange chews, lemon chews, and lime chews. She performs an experiment. Elizabeth randomly removes a chew from the bag, records the result, and returns the chew to the bag. Elizabeth performs the experiment 68 times. The results are shown below:
A orange chew was selected 44 times.
A lemon chew was selected 17 times.
A lime chew was selected 7 times.
If the experiment is repeated 1800 more times, about how many times would you expect Elizabeth to remove a orange chew from the bag? Round your answer to the nearest whole number.
Answer:

Elizabeth has a bag that contains orange chews, lemon chews, and lime chews. She performs an experiment. Elizabeth randomly removes a chew from the bag, records the result, and returns the chew to the bag. Elizabeth performs the experiment $68$ times. The results are shown below: $\newline$ A orange chew was selected $44$ times. $\newline$ A lemon chew was selected $17$ times. $\newline$ A lime chew was selected $7$ times. $\newline$ If the experiment is repeated $1800$ more times, about how many times would you expect Elizabeth to remove a orange chew from the bag? Round your answer to the nearest whole number. $\newline$ Answer:

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Experiment design

Full solution

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

68

times. The results are shown below:

\newline

A orange chew was selected

44

times.

\newline

A lemon chew was selected

17

times.

\newline

A lime chew was selected

7

times.

\newline

If the experiment is repeated

1800

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

\newline

Answer:

Determine Probability: Determine the probability of selecting an orange chew based on the initial experiment. $\newline$ To find the probability, we divide the number of times an orange chew was selected by the total number of experiments. $\newline$ Probability of selecting an orange chew $=$ Number of orange chews selected $/$ Total number of experiments $\newline$ Probability of selecting an orange chew $= \frac{44}{68}$
Calculate Decimal Probability: Calculate the probability as a decimal. $44 / 68 = 0.6471$ (rounded to four decimal places for accuracy in further calculations)
Estimate Selections in Additional Experiments: Use the probability to estimate the number of times an orange chew will be selected in the additional $1800$ experiments. $\newline$ Expected number of times an orange chew is selected = Probability of selecting an orange chew $*$ Number of additional experiments $\newline$ Expected number of times an orange chew is selected = $0.6471 \times 1800$
Perform Multiplication: Perform the multiplication to find the expected number of times an orange chew will be selected. $0.6471 \times 1800 \approx 1164.78$
Round to Nearest Whole Number: Round the result to the nearest whole number, as the question asks for an estimate. $\newline$ Rounded result = $1165$

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