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).

  1. Given Probability: The theoretical probability of getting a sum greater than 9 when rolling two dice is 636\frac{6}{36} (since there are 6 favorable outcomes and 36 total possible outcomes).

  2. Simplify the Probability: 636=16\frac{6}{36} = \frac{1}{6}.

  3. Number of Trials: The experiment is repeated 144 times.

  4. Expected Number of Successes: To predict how many times the sum will be greater than 9, multiply the probability by the number of trials: Expected Successes=16×144=24.\text{Expected Successes} = \frac{1}{6} \times 144 = 24.

So, the correct prediction is 24.

Let me know if you'd like more details or have any questions!

Here are 5 related questions for further exploration:

  1. What is the probability of rolling a sum of exactly 9?
  2. How many outcomes give a sum less than 5?
  3. What is the expected number of sums less than or equal to 7 if the experiment is repeated 100 times?
  4. What are all possible outcomes when rolling two dice?
  5. 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