To find \( P(A \cap B) \), we first need to determine the probabilities of events A and B.
Event A (landing on a number greater than 3 on the spinner):
- The spinner has numbers from 1 to 8. The numbers greater than 3 are 4, 5, 6, 7, and 8.
- There are 5 favorable outcomes (4, 5, 6, 7, 8) out of 8 possible outcomes.
- Therefore, \( P(A) = \frac{5}{8} \).
Event B (rolling a number greater than 3 on the number cube):
- The number cube has numbers from 1 to 6. The numbers greater than 3 are 4, 5, and 6.
- There are 3 favorable outcomes (4, 5, 6) out of 6 possible outcomes.
- Therefore, \( P(B) = \frac{3}{6} = \frac{1}{2} \).
Finding \( P(A \cap B) \): Since the spinner and the number cube operate independently, we can calculate the combined probability of both events occurring using the formula for the probability of independent events:
\[ P(A \cap B) = P(A) \times P(B) \]
Calculating it:
\[ P(A \cap B) = \frac{5}{8} \times \frac{1}{2} = \frac{5}{16} \]
Thus, the answer is:
\[ \boxed{\frac{5}{16}} \]