Question

If you 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.

Answer 1

To find the probability of landing on tails when flipping a coin and rolling an even number on a six-sided number cube simultaneously, we can break down the problem into two parts: the coin flip and the dice roll.

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

2. **Probability of rolling an even number:**
A six-sided number cube (die) has the numbers 1 through 6. The even numbers on a die are 2, 4, and 6. Thus, there are 3 favorable outcomes for rolling an even number out of a total of 6 possible outcomes. Therefore, the probability of rolling an even number is:
\[
P(\text{even}) = \frac{3}{6} = \frac{1}{2}
\]

3. **Finding the combined probability:**
Since the two events (flipping a coin and rolling a die) are independent, the combined probability of both events occurring is simply the product of their individual probabilities:
\[
P(\text{T and even}) = P(T) \times P(\text{even}) = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4}
\]

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