An experiment consists of throwing two four-faced dice (regular tetrahedra) with faces labeled 1, 2, 3, 4.

(a) Write down the sample space of this experiment.

(b) If A is the event 'total score is at least 4' list the outcomes belonging to A'.

(c) If each die is fair find the probability that the total score is at least 6 when the two dice are thrown. What is the probability that the total score is less than 6?

(d) What is the probability that a double: i.e. (1, 1),(2, 2),(3, 3),(4, 4) will not be thrown?

(e) What is the probability that a double is not thrown and the score is less than 6?