To find the probability \( P(A \cap B) \), we first need to determine the probabilities of events \( A \) and \( B \) and then the combined probability of both events happening simultaneously.
Event A (landing on a number greater than 3 on the spinner):
The numbers on the spinner are 1, 2, 3, 4, 5, 6, 7, and 8. The numbers greater than 3 are 4, 5, 6, 7, and 8.
There are 5 numbers greater than 3 and a total of 8 numbers on the spinner, so:
\[ P(A) = \frac{\text{Number of favorable outcomes for A}}{\text{Total outcomes for the spinner}} = \frac{5}{8} \]
Event B (rolling a number greater than 3 on the number cube):
The numbers on the cube are 1, 2, 3, 4, 5, and 6. The numbers greater than 3 are 4, 5, and 6.
There are 3 numbers greater than 3 and a total of 6 numbers on the cube, so:
\[ P(B) = \frac{\text{Number of favorable outcomes for B}}{\text{Total outcomes for the cube}} = \frac{3}{6} = \frac{1}{2} \]
Combining Events A and B:
Assuming that events A and B are independent (i.e., the outcome of the spinner does not affect the outcome of the cube), we can find the probability of both events occurring together using the rule for independent events:
\[ P(A \cap B) = P(A) \cdot P(B) \]
Substituting the probabilities we found:
\[ P(A \cap B) = \frac{5}{8} \cdot \frac{1}{2} = \frac{5}{16} \]
Thus, the probability \( P(A \cap B) \) is
\[ \boxed{\frac{5}{16}} \]