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)
Responses

112
1 over 12

18
1 eighth

16
1 sixth

14

Answer 1

To find the probability of spinning a B and rolling an even number, we need to calculate the probabilities of each event and then multiply them together since they are independent events.

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

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

3. **Combined probability**:
Since these two events are independent, we multiply their probabilities:
\[
P(B \text{ and even}) = P(B) \times P(\text{even}) = \frac{1}{4} \times \frac{1}{2} = \frac{1}{8}
\]

Thus, the probability of spinning a B and rolling an even number is:
\[
\frac{1}{8}
\]

The correct response is:
\(\frac{1}{8}\)