How is the probability of an even result found for a fair six-sided die?

Conditions

• The die is fair (each face has equal probability).
• The sample space is finite and consists of the numbers 1 through 6.
• The event of interest is rolling an even number.

Reasoning, step by step

1. Identify the sample space: $\{1, 2, 3, 4, 5, 6\}$.
2. Identify the favorable outcomes for the event 'even roll': $\{2, 4, 6\}$.
3. Count the number of favorable outcomes: 3.
4. Count the total number of possible outcomes: 6.
5. Apply the classical probability formula: $P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}$.
6. Calculate the ratio: $\frac{3}{6}$.
7. Simplify the fraction to get $\frac{1}{2}$.

Example

The video lists the numbers 1 through 6 vertically and circles 2, 4, and 6. The narration states: 'There are 3 favorable faces out of 6 equally likely faces, giving $3/6=1/2$.'

Common misconceptions

• Believing that the probability depends on the order of the numbers on the die.
• Confusing the number of favorable outcomes with the sum of the favorable outcomes.
• Assuming the die is biased without evidence, which would invalidate the classical probability formula.

Watch the explanation

Connected concepts

Explore next

• What is the probability of rolling an odd number?
• How does the probability change if the die has 8 sides?
• What is the probability of rolling a number greater than 4?

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