Working as in the previous exercise, answer the following questions:

(i) An urn contains 10 balls numbered 0–9. We select a ball at random, note the number on it, and return the ball into the urn. Then, we take out a second ball and also make a note of the number on that ball. What is the probability that

(a) the two numbers are the same?

(b) the sum of the two numbers equals 10?

(c) the difference between the two numbers is at least 6?

(d) the sum of the cubes of the two numbers exceeds 20?

(e) at least one of the two numbers is greater than or equal to 5?

(ii) In the experiment of tossing a coin five times, find the probability that

(a) at least three heads appear;

(b) heads turn up at least once;

(c) the first three outcomes of the coin are all heads;

(d) the first three outcomes of the coin are the same;

(e) heads appear in at least two successive tosses of the coin.