Shandra has a bag that contains pineapple chews, cherry chews, and peach chews. She performs an experiment. Shandra randomly removes a chew from the bag, records the result, and returns the chew to the bag. Shandra performs the experiment 57 times. The results are shown below:
A pineapple chew was selected 8 times.
A cherry chew was selected 25 times.
A peach chew was selected 24 times.
If the experiment is repeated 400 more times, about how many times would you expect Shandra to remove a pineapple chew from the bag? Round your answer to the nearest whole number.
From her experiment:
prob(pine) = 8/57
prob(cherry) = 25/57
prob(peach) = 24/57
expect (8/57)(400) pineapples to be picked, or appr 56 times
To find out how many times we would expect Shandra to remove a pineapple chew from the bag, we can use the concept of probability.
The probability of selecting a pineapple chew from the bag is given by the number of times a pineapple chew was selected divided by the total number of experiments performed.
Probability of selecting a pineapple chew = Number of times a pineapple chew was selected / Total number of experiments
Given that a pineapple chew was selected 8 times out of 57 experiments, the probability of selecting a pineapple chew is 8/57.
To find out how many times Shandra would expect to remove a pineapple chew out of 400 more experiments, we multiply the probability by the number of experiments.
Expected number of times to remove a pineapple chew = Probability of selecting a pineapple chew * Total number of additional experiments
Expected number of times to remove a pineapple chew = (8/57) * 400
Let's calculate the expected number of times to remove a pineapple chew:
(8/57) * 400 ≈ 56.14
Rounding the answer to the nearest whole number, we would expect Shandra to remove a pineapple chew from the bag about 56 times.
To find out how many times Shandra would expect to remove a pineapple chew from the bag, we can use the concept of probability.
First, let's calculate the probability of selecting a pineapple chew based on the first 57 experiments. We divide the number of times a pineapple chew was selected (8) by the total number of experiments (57):
Probability of selecting a pineapple chew = 8/57
Now, to estimate the number of times Shandra would expect to remove a pineapple chew in the next 400 experiments, we multiply the probability by the number of experiments:
Expected number of pineapple chews in the next 400 experiments = (8/57) * 400
To round the answer to the nearest whole number, we can use rounding rules. If the decimal part is less than 0.5, we round down; if it's 0.5 or greater, we round up.
Expected number of pineapple chews in the next 400 experiments ≈ 8/57 * 400 ≈ 56.14
Rounding 56.14 to the nearest whole number, we get:
Expected number of pineapple chews in the next 400 experiments ≈ 56
Therefore, we would expect Shandra to remove a pineapple chew from the bag about 56 times in the next 400 experiments.