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 find \( P(A \cap B) \), we first need to determine the probabilities of each individual event \( A \) and \( B \).

1. 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, 8.
   • The numbers greater than 3 are: 4, 5, 6, 7, 8.
   • There are 5 favorable outcomes (4, 5, 6, 7, 8) out of 8 possible outcomes.
   • Therefore, \[ P(A) = \frac{5}{8} \]

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

   • The numbers on the number cube are 1, 2, 3, 4, 5, 6.
   • The numbers greater than 3 are: 4, 5, 6.
   • There are 3 favorable outcomes (4, 5, 6) out of 6 possible outcomes.
   • Therefore, \[ P(B) = \frac{3}{6} = \frac{1}{2} \]

3. Finding \( P(A \cap B) \):

   • Assuming the spinner and cube are independent, we can find the joint probability \( P(A \cap B) \) by multiplying the probabilities of \( A \) and \( B \): \[ P(A \cap B) = P(A) \times P(B) = \frac{5}{8} \times \frac{1}{2} \] \[ = \frac{5 \times 1}{8 \times 2} = \frac{5}{16} \]

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

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