Question
you are tossing a coin and rolling a cube. what is the probability of obtaining tails and rolling a 3? enter your answer as a fraction
Answers
GPT-4o mini
To find the probability of obtaining tails when tossing a coin and rolling a 3 on a cube (standard six-sided die), we can calculate the probabilities of each event separately and then multiply them.
1. **Probability of obtaining tails when tossing a coin**:
- There are 2 possible outcomes when tossing a coin: heads (H) and tails (T).
- The probability of obtaining tails (T) is \( \frac{1}{2} \).
2. **Probability of rolling a 3 on a six-sided die**:
- There are 6 possible outcomes when rolling a die: 1, 2, 3, 4, 5, and 6.
- The probability of rolling a 3 is \( \frac{1}{6} \).
Now, we multiply the probabilities of the two independent events:
\[
P(\text{tails and rolling a 3}) = P(\text{tails}) \times P(\text{rolling a 3})
\]
\[
P(\text{tails and rolling a 3}) = \frac{1}{2} \times \frac{1}{6} = \frac{1}{12}
\]
Thus, the probability of obtaining tails and rolling a 3 is \(\frac{1}{12}\).
1. **Probability of obtaining tails when tossing a coin**:
- There are 2 possible outcomes when tossing a coin: heads (H) and tails (T).
- The probability of obtaining tails (T) is \( \frac{1}{2} \).
2. **Probability of rolling a 3 on a six-sided die**:
- There are 6 possible outcomes when rolling a die: 1, 2, 3, 4, 5, and 6.
- The probability of rolling a 3 is \( \frac{1}{6} \).
Now, we multiply the probabilities of the two independent events:
\[
P(\text{tails and rolling a 3}) = P(\text{tails}) \times P(\text{rolling a 3})
\]
\[
P(\text{tails and rolling a 3}) = \frac{1}{2} \times \frac{1}{6} = \frac{1}{12}
\]
Thus, the probability of obtaining tails and rolling a 3 is \(\frac{1}{12}\).