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Taub has a bag that contains pineapple chews, cherry chews, and peach 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 54 times. The results are shown below:
A pineapple chew was selected 35 times.
A cherry chew was selected 10 times.
A peach chew was selected 9 times.
If the experiment is repeated 800 more times, about how many times would you expect Taub to remove a cherry chew from the bag? Round your answer to the nearest whole number.
Answer:

Taub has a bag that contains pineapple chews, cherry chews, and peach 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 $54$ times. The results are shown below: $\newline$ A pineapple chew was selected $35$ times. $\newline$ A cherry chew was selected $10$ times. $\newline$ A peach chew was selected $9$ times. $\newline$ If the experiment is repeated $800$ more times, about how many times would you expect Taub to remove a cherry 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 pineapple chews, cherry chews, and peach 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

54

times. The results are shown below:

\newline

A pineapple chew was selected

35

times.

\newline

A cherry chew was selected

10

times.

\newline

A peach chew was selected

9

times.

\newline

If the experiment is repeated

800

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

\newline

Answer:

Calculate Probability of Cherry Chew: Determine the probability of selecting a cherry chew based on the initial experiment. $\newline$ The probability $P$ of selecting a cherry chew is calculated by dividing the number of times a cherry chew was selected by the total number of experiments. $\newline$ $P(\text{cherry chew}) = \frac{\text{Number of cherry chews selected}}{\text{Total number of experiments}}$ $\newline$ $P(\text{cherry chew}) = \frac{10}{54}$
Calculate Expected Number of Cherry Chews: Calculate the expected number of times a cherry chew will be selected in $800$ additional experiments. $\newline$ To find the expected number, multiply the probability of selecting a cherry chew by the number of additional experiments. $\newline$ Expected number of cherry chews $= P(\text{cherry chew}) \times \text{Additional experiments}$ $\newline$ Expected number of cherry chews $= \left(\frac{10}{54}\right) \times 800$
Perform Calculation for Expected Number: Perform the calculation to find the expected number of cherry chews. $\newline$ Expected number of cherry chews = $(10 / 54) \times 800$ $\newline$ Expected number of cherry chews $\approx 148.148148148$
Round Expected Number: Round the expected number to the nearest whole number. $\newline$ Expected number of cherry chews $\approx 148$ (rounded from $148.148148148$ )

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