Math Problem Statement
In a repeated experiment, Kim rolled a fair die twice. The theoretical probability of both rolls equaling a sum greater than 9 is 6 over 36. Predict how many times the rolls will result in a sum greater than 9 if the experiment is repeated 144 times.
24 12 9 6
Solution
To solve this problem, we need to apply the theoretical probability and scale it to the number of trials (144 experiments).
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Given Probability: The theoretical probability of getting a sum greater than 9 when rolling two dice is (since there are 6 favorable outcomes and 36 total possible outcomes).
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Simplify the Probability: .
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Number of Trials: The experiment is repeated 144 times.
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Expected Number of Successes: To predict how many times the sum will be greater than 9, multiply the probability by the number of trials:
So, the correct prediction is 24.
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Here are 5 related questions for further exploration:
- What is the probability of rolling a sum of exactly 9?
- How many outcomes give a sum less than 5?
- What is the expected number of sums less than or equal to 7 if the experiment is repeated 100 times?
- What are all possible outcomes when rolling two dice?
- How does the probability change if the dice are biased?
Tip: When calculating probabilities for repeated experiments, multiplying the probability of a single event by the number of trials is a key step.
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Math Problem Analysis
Mathematical Concepts
Probability
Theoretical Probability
Expected Value
Formulas
P(sum > 9) = 6/36
Expected Successes = Probability * Number of Trials
Theorems
Law of Large Numbers
Probability Theorem
Suitable Grade Level
Grades 6-8
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