Question
You are tossing a coin and rolling a number cube. What is the probability of obtaining tails and rolling a 3? Enter your answer as a fraction.
Answers
GPT-4o mini
To determine the probability of obtaining tails when tossing a coin and rolling a 3 on a number cube (which is a fair six-sided die), we will calculate the probabilities of each event separately and then multiply them together since these two events are independent.
1. **Probability of tossing tails**: A coin has two sides (heads and tails), so the probability of getting tails is:
\[
P(\text{tails}) = \frac{1}{2}
\]
2. **Probability of rolling a 3 on a number cube**: A standard number cube has six faces, numbered from 1 to 6. The probability of rolling any specific number (including 3) is:
\[
P(\text{rolling a 3}) = \frac{1}{6}
\]
3. **Combined Probability**: Since these two events are independent, we can multiply their probabilities:
\[
P(\text{tails and rolling a 3}) = P(\text{tails}) \times P(\text{rolling a 3}) = \frac{1}{2} \times \frac{1}{6} = \frac{1}{12}
\]
Thus, the probability of obtaining tails and rolling a 3 is
\[
\boxed{\frac{1}{12}}
\]
1. **Probability of tossing tails**: A coin has two sides (heads and tails), so the probability of getting tails is:
\[
P(\text{tails}) = \frac{1}{2}
\]
2. **Probability of rolling a 3 on a number cube**: A standard number cube has six faces, numbered from 1 to 6. The probability of rolling any specific number (including 3) is:
\[
P(\text{rolling a 3}) = \frac{1}{6}
\]
3. **Combined Probability**: Since these two events are independent, we can multiply their probabilities:
\[
P(\text{tails and rolling a 3}) = P(\text{tails}) \times P(\text{rolling a 3}) = \frac{1}{2} \times \frac{1}{6} = \frac{1}{12}
\]
Thus, the probability of obtaining tails and rolling a 3 is
\[
\boxed{\frac{1}{12}}
\]