What is the probability of rolling a 6 on a standard 6-sided die, then rolling a 3 on the same die? Round your answer to the nearest tenth if necessary.

The probability of rolling a 6 on a standard 6-sided die is:

\[
P(\text{6}) = \frac{1}{6}
\]

The probability of rolling a 3 on the same die is also:

\[
P(\text{3}) = \frac{1}{6}
\]

Since these are independent events, the combined probability of both events happening (rolling a 6 followed by a 3) is the product of the individual probabilities:

\[
P(\text{6 then 3}) = P(\text{6}) \times P(\text{3}) = \frac{1}{6} \times \frac{1}{6} = \frac{1}{36}
\]

Therefore, the probability is \( \frac{1}{36} \), which is approximately:

\[
\frac{1}{36} \approx 0.0278
\]

Rounding to the nearest tenth:

\[
0.0278 \approx 0.03
\]

So, the probability is **0.03**.

Would you like more details, or do you have any questions?

Here are 5 related questions to explore:
1. What is the probability of rolling any specific number twice in a row on a 6-sided die?
2. How do you calculate the probability of rolling two different specific numbers in sequence?
3. If you roll a die three times, what is the probability of rolling a 6, 3, and 5 in that order?
4. How does the probability change if you use an 8-sided die instead of a 6-sided one?
5. What is the expected number of rolls to get a 6 followed by a 3?

**Tip**: In probability, when dealing with independent events, the combined probability is the product of the individual probabilities.

Discover the probability of rolling a 6 followed by a 3 on a standard 6-sided die. This problem demonstrates the multiplication rule for independent events, with a final probability of approximately 0.03. Ideal for students in Grades 6-8.

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