What is the theoretical probability of flipping a heads and then rolling the dice and getting a 2?

To find the theoretical probability of flipping a heads and then rolling a dice and getting a 2, we need to calculate the probability of each independent event:

1. **Probability of flipping a heads**: Since a coin has two sides, the probability of flipping a heads is:
   \[
   P(\text{Heads}) = \frac{1}{2}
   \]

2. **Probability of rolling a 2 on a six-sided die**: Since a die has 6 faces, the probability of rolling a 2 is:
   \[
   P(\text{Rolling a 2}) = \frac{1}{6}
   \]

Since these two events (flipping a coin and rolling a die) are independent, the total probability of both events occurring in sequence (flipping heads and then rolling a 2) is the product of their individual probabilities:
\[
P(\text{Heads and Rolling a 2}) = P(\text{Heads}) \times P(\text{Rolling a 2}) = \frac{1}{2} \times \frac{1}{6} = \frac{1}{12}
\]

Thus, the theoretical probability of flipping heads and then rolling a 2 is \( \frac{1}{12} \).

Would you like more details or have any other questions?

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Here are 5 related questions to expand on this:
1. What is the probability of flipping tails and then rolling a 4?
2. How would the probability change if the die had 8 sides?
3. What is the probability of flipping two heads in a row?
4. What is the probability of rolling an odd number on the die?
5. How would you calculate the probability of flipping a heads and rolling an odd number?

**Tip**: When calculating probabilities of independent events, always multiply the individual probabilities together.

Discover how to calculate the theoretical probability of flipping a coin and getting heads, then rolling a six-sided die and landing on a 2. This problem covers key probability concepts, including the multiplication rule for independent events. Suitable for students in Grades 6-8.

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