To determine the probability that Kayla rolls an even number on a die and gets heads on a coin toss, we need to follow these steps:
1. Determine the Probability of Rolling an Even Number on a Die:
- A standard die has six faces, numbered 1 through 6.
- The even numbers on a die are 2, 4, and 6.
- Therefore, there are 3 even numbers out of 6 possible outcomes.
Thus, the probability of rolling an even number is:
[tex]\[
\frac{\text{Number of even numbers}}{\text{Total possible outcomes}} = \frac{3}{6} = 0.5
\][/tex]
2. Determine the Probability of Getting Heads on a Coin Toss:
- A coin has two faces: heads and tails.
- There are 1 heads out of 2 possible outcomes.
Hence, the probability of getting heads is:
[tex]\[
\frac{\text{Number of heads}}{\text{Total possible outcomes}} = \frac{1}{2} = 0.5
\][/tex]
3. Calculate the Combined Probability of Both Independent Events:
- The events (rolling a die and tossing a coin) are independent, which means the probability of both events occurring is the product of their individual probabilities.
Therefore, the combined probability is:
[tex]\[
\text{Probability of even number and heads} = \text{Probability of even number} \times \text{Probability of heads} = 0.5 \times 0.5 = 0.25
\][/tex]
4. Convert the Probability into a Fraction:
- The probability of 0.25 can be expressed as [tex]\(\frac{1}{4}\)[/tex].
Thus, the probability that Kayla rolls an even number and gets heads is [tex]\(\frac{1}{4}\)[/tex].
The correct answer is:
[tex]\[
\boxed{\frac{1}{4}}
\][/tex]
