To determine the probability that Jason rolls a 3 on a fair number cube and flips heads on a coin, we need to consider the individual probabilities of each event and then find the combined probability of both events happening together.
1. Probability of rolling a 3 on a fair number cube:
- A fair number cube (also known as a die) has 6 faces, each numbered from 1 to 6.
- The outcome of rolling a 3 is just one of these 6 equally likely outcomes.
- Therefore, the probability of rolling a 3 is:
[tex]\[
\text{Probability of rolling a 3} = \frac{1}{6}
\][/tex]
2. Probability of flipping heads on a fair coin:
- A fair coin has 2 faces: heads and tails.
- The outcome of flipping heads is one of the 2 equally likely outcomes.
- Thus, the probability of flipping heads is:
[tex]\[
\text{Probability of flipping heads} = \frac{1}{2}
\][/tex]
3. Combined probability of both events happening:
- Since the roll of the number cube and the flip of the coin are independent events, we can find the combined probability by multiplying the individual probabilities of each event.
- Therefore, the combined probability is:
[tex]\[
\text{Combined Probability} = \left( \frac{1}{6} \right) \times \left( \frac{1}{2} \right) = \frac{1}{12}
\][/tex]
So, the probability that Jason rolls a 3 and flips heads is:
[tex]\[
\boxed{\frac{1}{12}}
\][/tex]
