i. Two six-sided dice are rolled and the scores added together. Draw the sample space, the probability density function and the cumulative probability density function by hand.

ii. What is the probability that the number obtained on one of the dice is a multiple of a number obtained on the other dice? What is the probability of doubles (1,1, 2,2. etc)?

iii. A weekly lottery with numbers 1-49 has come up with the numbers 2,4,6,8,10 and 20,25,30,35,40 over the last month. There have been claims of fraud and the organisers are worried as ticket sales are down.