Desmond is rolling standard six sided dice. He plans to roll it 72 times. Approximately how many times would you expect him to roll an even number and why?
Understand the Problem
The question is asking for the expected frequency of rolling even numbers (2, 4, or 6) when a six-sided die is rolled 72 times. To solve this, we calculate the probability of rolling an even number and then multiply it by the total number of rolls to find the expected count.
Answer
36
Answer for screen readers
The expected frequency of rolling even numbers when a six-sided die is rolled 72 times is 36.
Steps to Solve
- Determine the probability of rolling an even number
A standard six-sided die has three even numbers: 2, 4, and 6. Therefore, the probability of rolling an even number is given by:
$$ P(\text{even}) = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} $$
Substituting in the values:
$$ P(\text{even}) = \frac{3}{6} = \frac{1}{2} $$
- Calculate the expected frequency
The expected frequency of rolling even numbers can be calculated by multiplying the probability of rolling an even number by the total number of rolls (72):
$$ \text{Expected frequency} = P(\text{even}) \times \text{Total rolls} $$
Substituting the values:
$$ \text{Expected frequency} = \frac{1}{2} \times 72 = 36 $$
The expected frequency of rolling even numbers when a six-sided die is rolled 72 times is 36.
More Information
This means that if you roll a six-sided die 72 times, you can reasonably expect to roll an even number about 36 times. This result helps illustrate the concept of probability in a practical scenario.
Tips
- Forgetting to account for the total number of even faces on the die.
- Miscalculating the probability by using the wrong number of outcomes; ensure you always count the total faces correctly.
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