Complete a two-card sample space and calculate probabilities, expectation and a game value.

Two boxes contain numbered cards as shown below.

Two cards are drawn at random, one from each box.

1. Copy and complete the table below to show all nine equally likely outcomes

   [2]

   \((3,9)\)
   \((3,10)\)
   \((3,10)\)

   Let \(S\) be the sum of the numbers on the two cards.

2. Write down all the possible values of \(S\).

   [2]

3. Find the probability of each value of \(S\).

   [2]

4. Find the expected value of \(S\).

   [3]

5. Anna plays a game where she wins \(\$50\) if \(S\) is even and loses \(\$30\) if \(S\) is odd. Anna plays the game \(36\) times. Find the amount she expects to have at the end of the \(36\) games.

   [3]