Question

A coin is flipped, then a 6-sided die is rolled. What is the probability of getting heads and an even number? (1 point) Responses 12 1 2 14 1 4 16 1 6 112

Answer 1

To calculate the probability of getting heads from flipping a coin and rolling an even number on a 6-sided die, we will break it down into two parts.

1. **Probability of getting heads when flipping a coin:**
- There are 2 outcomes when flipping a coin: heads (H) and tails (T).
- The probability of getting heads (P(H)) is:
\[
P(H) = \frac{1}{2}
\]

2. **Probability of rolling an even number on a 6-sided die:**
- The even numbers on a 6-sided die are 2, 4, and 6. There are 3 even outcomes.
- The total number of outcomes when rolling a die is 6.
- The probability of rolling an even number (P(Even)) is:
\[
P(Even) = \frac{3}{6} = \frac{1}{2}
\]

3. **Combined probability:**
- Since the coin flip and die roll are independent events, the total probability of both occurring (getting heads and rolling an even number) can be calculated by multiplying the individual probabilities:
\[
P(H \text{ and } Even) = P(H) \times P(Even) = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4}
\]

Thus, the probability of getting heads and an even number is \(\frac{1}{4}\).

The response corresponding to this probability is:
\[
\frac{1}{4}
\]