We are asked to find the probability of rolling a number greater than 4 or less than 3 on a single die.

Step-by-Step Solution:

A die has 6 faces with numbers: 1, 2, 3, 4, 5, and 6. The possible outcomes are {1, 2, 3, 4, 5, 6}.

Condition 1: Numbers greater than 4

The numbers greater than 4 are 5 and 6.

Condition 2: Numbers less than 3

The numbers less than 3 are 1 and 2.

We are asked to find the probability of either event happening, so we look at the union of these two sets.

• Greater than 4: {5, 6}
• Less than 3: {1, 2}

The total favorable outcomes are: {1, 2, 5, 6}, which gives us 4 favorable outcomes.

Total possible outcomes:

Since a die has 6 faces, the total number of possible outcomes is 6.

Probability:

The probability of rolling a number greater than 4 or less than 3 is:

$P = \frac{\text{favorable outcomes}}{\text{total outcomes}} = \frac{4}{6} = \frac{2}{3}$

Thus, the probability is $\frac{2}{3}$.

Would you like more details or have any questions?

Related Questions:

1. What is the probability of rolling a number less than 5 on a die?
2. How would the probability change if you rolled two dice?
3. What is the probability of rolling an even number on a single die?
4. How do you calculate probabilities for compound events in dice rolling?
5. What is the probability of rolling a 1 or a 6 on a single die?

Tip:

When calculating probabilities for compound events (like "or" statements), always check if there is any overlap in outcomes to avoid double-counting.