A biased die in the shape of a pyramid has five faces marked 1, 2, 3, 4 and 5. The possible scores are 1, 2, 3, 4 and 5 and p(x) = k – x/25, where k is a constant.

a. Find, in terms of k, the probability of scoring:

i. 5

ii. Less than 3.

b. The die is rolled three times and the scores are added together. Evaluate k and find the probability that the sum of the three scores is less than 5.