Validate and solve three discrete probability distributions.

Three students, Kim, Ching Li and Jonathan, each have a pack of cards from which they select a card at random. Each card has a 0, 3, 4 or 9 printed on it.

1. Kim states that the probability distribution for her pack of cards is shown below. Explain why Kim is incorrect.[2]

   \(x\)	0	3	4	9
   \(P(X=x)\)	0.3	0.45	0.2	0.35

2. Ching Li correctly states that the probability distribution for her pack of cards is shown below. Find the value of \(k\).[2]

   \(x\)	0	3	4	9
   \(P(X=x)\)	0.4	\(k\)	\(2k\)	0.3

3. Jonathan correctly states that the probability distribution for his pack of cards is given by \(P(X=x)=\frac{x+1}{20}\). One card is drawn at random from his pack.[4]
   1. Calculate the probability that the number on the card drawn is 0.
   2. Calculate the probability that the number on the card drawn is greater than 0.