4 A pack of \(k\) cards is labelled \(1,2 , \ldots , k\). A card is drawn at random from the pack. The random variable \(X\) represents the number on the card.
- Given that \(k > 10\), find \(\mathrm { P } ( X \geqslant 10 )\).
You are now given that \(k = 20\).
- A card is drawn at random from the pack and the number on it is noted. The card is then returned to the pack. This process is repeated until the second occasion on which the number noted is less than 9 .
Find the probability that no more than 4 cards have to be drawn.
Answer all the questions.
Section B (95 marks)