Question

A spinner is divided into 4 equal sections labeled A, B, C, and D. A fair six-sided die is also rolled. What is the probability of spinning a B and rolling an even number?(1 point)

Answer 1

To find the probability of two independent events occurring (spinning a B and rolling an even number), we will calculate the probabilities of each event separately and then multiply them.

1. **Probability of spinning a B:**
The spinner is divided into 4 equal sections labeled A, B, C, and D. Therefore, the probability of landing on B is:
\[
P(B) = \frac{1}{4}
\]

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

3. **Combining the two probabilities:**
Since spinning the spinner and rolling the die are independent events, the combined probability is:
\[
P(B \text{ and Even}) = P(B) \times P(\text{Even}) = \frac{1}{4} \times \frac{1}{2} = \frac{1}{8}
\]

Thus, the probability of spinning a B and rolling an even number is \(\frac{1}{8}\).