Question

If you toss a coin and roll a number cube, what is the probability of obtaining a head and rolling a 6? Round your answer to the nearest hundredth if using a decimal.(1 point)

Answer 1

To find the probability of obtaining a head when tossing a coin and rolling a 6 on a number cube (which has the numbers 1 through 6), we can follow these steps:

1. **Probability of tossing a head**: A coin has 2 sides (heads and tails), so the probability of getting a head is:
\[
P(\text{Head}) = \frac{1}{2}
\]

2. **Probability of rolling a 6**: A standard number cube (die) has 6 faces, so the probability of rolling a 6 is:
\[
P(6) = \frac{1}{6}
\]

3. **Combine the probabilities**: The events of tossing the coin and rolling the die are independent, so we multiply their probabilities to find the probability of both occurring:
\[
P(\text{Head and 6}) = P(\text{Head}) \times P(6) = \frac{1}{2} \times \frac{1}{6} = \frac{1}{12}
\]

4. **Convert to decimal**: To express \(\frac{1}{12}\) as a decimal:
\[
\frac{1}{12} \approx 0.0833
\]

5. **Round to the nearest hundredth**: Rounding \(0.0833\) to the nearest hundredth gives:
\[
0.08
\]

Thus, the final answer is:
\[
\boxed{0.08}
\]