7 Rory has 10 cards. Four of the cards have a 3 printed on them and six of the cards have a 4 printed on them. He takes three cards at random, without replacement, and adds up the numbers on the cards.
- Show that P (the sum of the numbers on the three cards is \(11 ) = \frac { 1 } { 2 }\).
- Draw up a probability distribution table for the sum of the numbers on the three cards.
Event \(R\) is 'the sum of the numbers on the three cards is 11 '. Event \(S\) is 'the number on the first card taken is a \(3 ^ { \prime }\).
- Determine whether events \(R\) and \(S\) are independent. Justify your answer.
- Determine whether events \(R\) and \(S\) are exclusive. Justify your answer.