A bag contains 3 red and 4 white balls. Another bag contains 5 red and 6 white balls. A bag is chosen by throwing a die. If the die shows 6, the first bag is chosen, otherwise the second bag is chosen

Step 1: Define events and probabilities for part 9.a).
Let $G$ be the event that the gold urn is selected.
Let $S$ be the event that the silver urn is selected.
Let $R$ be the event that a red ball is selected.

The die shows 6 for the gold urn, so $P(G) = \frac{1}{6}$.
Otherwise (1, 2, 3, 4, 5) for the silver urn, so $P(S) = \frac{5}{6}$.

Gold urn contains 3 red balls and 4 white balls, for a total of 7 balls.
The probability of selecting a red ball from the gold urn is $P(R|