To find the probability of rolling an odd number or a number less than 5 on a six-sided die, let's break it down step by step:

Step 1: List the outcomes on the die.

The possible outcomes when rolling a six-sided die are:
$\{1, 2, 3, 4, 5, 6\}$

Step 2: Identify the outcomes for each event.

Event 1: Rolling an odd number.

The odd numbers on the die are: $\{1, 3, 5\}$

Event 2: Rolling a number less than 5.

The numbers less than 5 on the die are: $\{1, 2, 3, 4\}$

Step 3: Find the union of the two events.

We need to find the outcomes that are in either of the two events. This is the union of the two sets:

• Odd numbers: {1, 3, 5}
• Numbers less than 5: {1, 2, 3, 4}

The union of these two sets is: $\{1, 2, 3, 4, 5\}$ (The number 6 is excluded because it does not fit either condition.)

Step 4: Count the favorable outcomes.

The favorable outcomes are:
$\{1, 2, 3, 4, 5\}$ There are 5 favorable outcomes.

Step 5: Calculate the probability.

The probability is the number of favorable outcomes divided by the total number of possible outcomes. Since there are 6 possible outcomes (the numbers 1 through 6), the probability is: $P(\text{odd or less than 5}) = \frac{5}{6}$

Final Answer:

The probability of rolling an odd number or a number less than 5 is $\frac{5}{6}$.

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Would you like further details or clarification on this? Here are some related questions for exploration:

1. What is the probability of rolling a number greater than or equal to 4?
2. What is the probability of rolling a prime number?
3. How does the probability change if the die has more sides?
4. What is the probability of rolling an even number or a number less than 4?
5. What is the probability of rolling a number that is both odd and less than 5?

Tip: Always check if an event overlaps with another to avoid double-counting outcomes when calculating probabilities for "or" events.