Math Problem Statement

Alang has a bag that contains pineapple chews, strawberry chews, and lime chews. He performs an experiment. Alang randomly removes a chew from the bag, records the result, and returns the chew to the bag. Alang performs the experiment 26 times. The results are shown below:

A pineapple chew was selected 20 times.

A strawberry chew was selected 4 times.

A lime chew was selected 2 times.

Based on these results, express the probability that the next chew Alang removes from the bag will be lime chew as a fraction in simplest form.

Solution

To find the probability that the next chew Alang removes from the bag will be a lime chew, we can use the relative frequency approach. The probability is given by the ratio of the number of times a lime chew was selected to the total number of experiments performed.

Steps:

  1. Total number of experiments: Alang performed the experiment 26 times.
  2. Number of lime chews selected: A lime chew was selected 2 times.
  3. Probability of selecting a lime chew: P(lime chew)=Number of lime chews selectedTotal number of experiments=226P(\text{lime chew}) = \frac{\text{Number of lime chews selected}}{\text{Total number of experiments}} = \frac{2}{26}
  4. Simplify the fraction: 226=113\frac{2}{26} = \frac{1}{13}

Thus, the probability that the next chew Alang removes from the bag will be a lime chew is 113\frac{1}{13}.

Would you like further clarification or details on how to approach similar problems? Here are some additional related questions:

  1. How would the probability change if the number of experiments was increased to 100?
  2. What is the probability of selecting a pineapple chew based on the results?
  3. If Alang removed 10 pineapple chews, how would the probability of picking a pineapple chew change?
  4. How can the experimental probability be compared to theoretical probability if the true ratios of the chews were known?
  5. What would happen to the probability of selecting a lime chew if 3 more lime chews were added to the bag?

Tip: When solving probability problems, always ensure the fraction is in simplest form for clarity and accuracy.

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Math Problem Analysis

Mathematical Concepts

Probability
Relative Frequency

Formulas

P(lime chew) = Number of lime chews selected / Total number of experiments

Theorems

Law of Large Numbers (for experimental probability)

Suitable Grade Level

Grades 5-7