A single die has 6 faces numbered from 1 to 6. Each face has an equal probability of appearing when the die is rolled, which is $\frac{1}{6}$.

(a) Probability of obtaining a 3:

There is only one outcome where the die shows 3. Since there are 6 possible outcomes, the probability of obtaining a 3 is: $P(3) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{1}{6}.$

(b) Probability of obtaining an odd number:

The odd numbers on a die are $1, 3,$ and $5$. Therefore, there are 3 favorable outcomes. The probability of obtaining an odd number is: $P(\text{odd}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{3}{6} = \frac{1}{2}.$

Final Answers:

• (a) $P(3) = \frac{1}{6}$
• (b) $P(\text{odd}) = \frac{1}{2}$

Would you like further clarification or assistance with related problems?

Related Questions:

1. What is the probability of rolling a number greater than 4?
2. What is the probability of rolling an even number?
3. How would the probabilities change if using an 8-sided die?
4. What is the probability of rolling a prime number on a standard die?
5. How would you calculate the expected value of a single roll of a die?

Tip:

Always start by identifying the total number of outcomes and the favorable outcomes to solve probability problems systematically.