Question

If your flip one coin and roll one six-sided number cube, find the probability of landing on tails and rolling an even number at the same time. Write your answer as a simplified fraction.

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Answer 1

To find the probability of landing on tails and rolling an even number at the same time, we first calculate the individual probabilities.

1. **Probability of landing on tails when flipping a coin**:
A standard coin has two sides: heads and tails. Thus, the probability of landing on tails is:
\[
P(\text{tails}) = \frac{1}{2}
\]

2. **Probability of rolling an even number on a six-sided number cube**:
The even numbers on a six-sided die are 2, 4, and 6. There are three even numbers out of a total of six numbers. Therefore, the probability of rolling an even number is:
\[
P(\text{even number}) = \frac{3}{6} = \frac{1}{2}
\]

3. **Probability of both events happening at the same time**:
Since the coin flip and the die roll are independent events, we can find the combined probability by multiplying the probabilities of each event:
\[
P(\text{tails and even}) = P(\text{tails}) \times P(\text{even number}) = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4}
\]

Thus, the probability of landing on tails and rolling an even number at the same time is:
\[
\boxed{\frac{1}{4}}
\]