Math Problem Statement

Liam has a bag that contains pineapple chews, cherry chews, and lime chews. He performs an experiment. Liam randomly removes a chew from the bag, records the result, and returns the chew to the bag. Liam performs the experiment 62 times. The results are shown below: A pineapple chew was selected 58 times. A cherry chew was selected 2 times. A lime chew was selected 2 times.

Based on these results, express the probability that the next chew Liam removes from the bag will be cherry chew as a decimal to the nearest hundredth

Solution

To calculate the probability that the next chew Liam removes will be a cherry chew, we can use the relative frequency of cherry chews based on the results from the experiment.

The probability is given by:

Probability of cherry chew=Number of cherry chews selectedTotal number of experiments performed\text{Probability of cherry chew} = \frac{\text{Number of cherry chews selected}}{\text{Total number of experiments performed}}

From the problem:

  • Number of cherry chews selected = 2
  • Total number of experiments = 62

Now, calculate the probability:

Probability of cherry chew=2620.03226\text{Probability of cherry chew} = \frac{2}{62} \approx 0.03226

Rounding this to the nearest hundredth:

Probability of cherry chew0.03\text{Probability of cherry chew} \approx 0.03

So, the probability that the next chew will be a cherry chew is 0.03 (to the nearest hundredth).

Would you like any further clarification? Here are some related questions to explore:

  1. How can we calculate the probability for pineapple chews?
  2. How do we determine the probability for lime chews in this experiment?
  3. What would the probability of selecting a pineapple chew be if the experiment was repeated 100 times?
  4. How would you express this probability as a percentage?
  5. What is the concept of "relative frequency" in probability?

Tip: The more times you repeat an experiment, the more accurate the probability estimate will be!

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Math Problem Analysis

Mathematical Concepts

Probability
Relative Frequency

Formulas

Probability = (Number of desired outcomes) / (Total number of outcomes)

Theorems

Law of Large Numbers

Suitable Grade Level

Grades 6-8