To determine the probability of two independent events happening together, we first find the probability of each event separately and then multiply these probabilities.
1. Probability of rolling a 4 on a number cube (die):
- A standard number cube has 6 faces, each showing a different number from 1 to 6.
- The event of rolling a 4 can occur in one out of these 6 possible outcomes.
- Therefore, the probability of rolling a 4 is \(\frac{1}{6}\).
2. Probability of flipping tails on a coin:
- A coin has two sides: heads and tails.
- The event of flipping tails can occur in one out of these 2 possible outcomes.
- Therefore, the probability of flipping tails is \(\frac{1}{2}\).
3. Combined probability of both events happening:
- These two events (rolling a 4 on a die and flipping tails on a coin) are independent events.
- To find the combined probability, we multiply the probability of each individual event:
[tex]\[
\text{Combined Probability} = \left(\frac{1}{6}\right) \times \left(\frac{1}{2}\right)
\][/tex]
Now, let's carry out the multiplication:
[tex]\[
\text{Combined Probability} = \frac{1}{6} \times \frac{1}{2} = \frac{1 \times 1}{6 \times 2} = \frac{1}{12}
\][/tex]
Therefore, the probability of rolling a 4 on a number cube and flipping tails on a coin is \(\frac{1}{12}\).
The correct answer is:
A) [tex]\(\frac{1}{12}\)[/tex]
