Math Problem Statement

the table shows the outcome of rolling a number cube (labeled 1 through 6 200 times Income 1 2 3 4 5 6 outcome 20 28 35 33 38 36 based on the outcomes, enter the number of times the cube is expected to land on 1 if it is rolled 50 times Enter your answer as a number, like this: 42

Solution

To find the expected number of times the cube will land on 1 when rolled 50 times, we can use the proportion from the original outcomes.

The proportion of times the cube landed on 1 out of 200 rolls is:

20200=0.1\frac{20}{200} = 0.1

Now, to find the expected number of times the cube will land on 1 in 50 rolls, we multiply this proportion by 50:

0.1×50=50.1 \times 50 = 5

So, the expected number of times the cube will land on 1 in 50 rolls is 5.


Would you like more details on how to calculate expected values? Or do you have another question?

  1. What is the general formula for calculating expected value?
  2. How do you calculate the probability of rolling a specific number on a fair number cube?
  3. How does the expected value change when the number of rolls is different?
  4. What would happen if the cube is biased and the outcomes aren't equally likely?
  5. How could you use a probability distribution to predict outcomes over multiple trials?

Tip: Always check if the outcomes from your experiment match the theoretical probabilities before making predictions!

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Math Problem Analysis

Mathematical Concepts

Probability
Expected Value
Proportions

Formulas

Expected Value = Proportion of event × Total trials

Theorems

Law of Large Numbers

Suitable Grade Level

Grades 7-9