a. Find the probability that when a single​ six-sided die is​ rolled, the outcome is 3.
b. Find the probability that when a coin is​ tossed, the result is tails.
c. Find the probability that when a​ six-sided die is​ rolled, the outcome is 9.

Let's break down the probability of each scenario:

**a. Probability of rolling a 3 on a six-sided die:**

A standard six-sided die has six possible outcomes: \( \{1, 2, 3, 4, 5, 6\} \). The probability of rolling any specific number (like 3) is given by:

\[
P(\text{rolling a 3}) = \frac{\text{number of favorable outcomes}}{\text{total number of possible outcomes}} = \frac{1}{6}
\]

So, the probability is \( \frac{1}{6} \).

---

**b. Probability of getting tails on a coin toss:**

A standard coin has two outcomes: heads or tails. The probability of getting tails is:

\[
P(\text{getting tails}) = \frac{1}{2}
\]

So, the probability is \( \frac{1}{2} \).

---

**c. Probability of rolling a 9 on a six-sided die:**

A six-sided die only has outcomes \( \{1, 2, 3, 4, 5, 6\} \). Since rolling a 9 is not possible on a six-sided die, the probability of this event is 0:

\[
P(\text{rolling a 9}) = 0
\]

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### Summary of results:
- **a.** \( P(\text{rolling a 3}) = \frac{1}{6} \)
- **b.** \( P(\text{getting tails}) = \frac{1}{2} \)
- **c.** \( P(\text{rolling a 9}) = 0 \)

Would you like more details on any of these concepts?

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Here are five related questions you could explore:

1. What is the probability of rolling an even number on a six-sided die?
2. What is the probability of rolling a number greater than 4 on a six-sided die?
3. If you roll two six-sided dice, what is the probability of getting a sum of 7?
4. What is the probability of flipping two heads in a row with a coin?
5. What is the probability of rolling a 1 or a 6 on a six-sided die?

**Tip:** When calculating probability, always remember to count all possible outcomes carefully to ensure accuracy!

Explore how to calculate the probability of rolling a 3 on a six-sided die, getting tails on a coin toss, and understanding impossible events like rolling a 9 on a six-sided die. This problem covers basic probability concepts suitable for Grades 5-7.

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