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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 6969 times. The results are shown below:\newlineA orange chew was selected 5757 times.\newlineA apple chew was selected 88 times.\newlineA lime chew was selected 44 times.\newlineIf the experiment is repeated 20002000 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.\newlineAnswer:

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 6969 times. The results are shown below:\newlineA orange chew was selected 5757 times.\newlineA apple chew was selected 88 times.\newlineA lime chew was selected 44 times.\newlineIf the experiment is repeated 20002000 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.\newlineAnswer:
  1. Calculate Probability: Determine the probability of selecting an apple chew based on the initial experiment.\newlineTaub selected an apple chew 88 times out of 6969 total selections.\newlineProbability of selecting an apple chew == Number of apple chews selected // Total number of selections\newlineProbability of selecting an apple chew =869= \frac{8}{69}
  2. Estimate Selections in 20002000 Experiments: Use the probability to estimate the number of times an apple chew would be selected in 20002000 additional experiments.\newlineExpected number of times an apple chew is selected = Probability of selecting an apple chew ×\times Number of additional experiments\newlineExpected number of times an apple chew is selected = (8/69)×2000(8 / 69) \times 2000
  3. Calculate Expected Selections: Calculate the expected number of times an apple chew is selected.\newlineExpected number of times an apple chew is selected = (8/69)×2000(8 / 69) \times 2000\newlineExpected number of times an apple chew is selected (0.11594202898550725)×2000\approx (0.11594202898550725) \times 2000\newlineExpected number of times an apple chew is selected 231.8840579710145\approx 231.8840579710145
  4. Round to Nearest Whole Number: Round the result to the nearest whole number, as the question asks for an estimate.\newlineExpected number of times an apple chew is selected 232\approx 232 (rounded to the nearest whole number)

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