Question

Consider a spinner with numbers 1–8 and a number cube with numbers 1–6. Let event A
represent landing on a number greater than 3 on the spinner and event B
represent rolling a number greater than 3 on the number cube. Find P(A∩B)
. Enter your response as a fraction.(1 point)

Answer 1

To determine \( P(A \cap B) \), we first need to find the probabilities of events \( A \) and \( B \).

**Event A**: Landing on a number greater than 3 on the spinner.

The numbers on the spinner are 1 through 8. The numbers greater than 3 are 4, 5, 6, 7, and 8. Therefore, there are 5 favorable outcomes.

\[
P(A) = \frac{\text{Number of favorable outcomes for A}}{\text{Total outcomes on the spinner}} = \frac{5}{8}
\]

**Event B**: Rolling a number greater than 3 on the number cube.

The numbers on the cube are 1 through 6. The numbers greater than 3 are 4, 5, and 6. Therefore, there are 3 favorable outcomes.

\[
P(B) = \frac{\text{Number of favorable outcomes for B}}{\text{Total outcomes on the number cube}} = \frac{3}{6} = \frac{1}{2}
\]

Since the spinner and the number cube operate independently, we can find \( P(A \cap B) \) by multiplying the probabilities of events \( A \) and \( B \):

\[
P(A \cap B) = P(A) \cdot P(B) = \left( \frac{5}{8} \right) \cdot \left( \frac{1}{2} \right) = \frac{5}{16}
\]

Thus, the probability \( P(A \cap B) \) is

\[
\boxed{\frac{5}{16}}
\]