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:
- Total number of experiments: Alang performed the experiment 26 times.
- Number of lime chews selected: A lime chew was selected 2 times.
- Probability of selecting a lime chew:
- Simplify the fraction:
Thus, the probability that the next chew Alang removes from the bag will be a lime chew is .
Would you like further clarification or details on how to approach similar problems? Here are some additional related questions:
- How would the probability change if the number of experiments was increased to 100?
- What is the probability of selecting a pineapple chew based on the results?
- If Alang removed 10 pineapple chews, how would the probability of picking a pineapple chew change?
- How can the experimental probability be compared to theoretical probability if the true ratios of the chews were known?
- 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