Two urns, G and S, contain R and W balls. A die roll selects G if 6, otherwise S. What are the probabilities for subsequent draws?

Here are the solutions for parts c), d), and e) of the question.

Step 1: Understand the scenario for parts c), d), and e).
The problem describes two urns:

• Gold Urn (G): 3 Red (R) balls, 4 White (W) balls. Total = 7 balls.
• Silver Urn (S): 5 Red (R) balls, 2 White (W) balls. Total = 7 balls.

A die is rolled:

• If it shows 6, the Gold Urn is selected. $P(G) = \frac{1}{6}$.
• Otherwise (1, 2, 3, 4, 5),