1.9 An experiment consists of rolling two dice simultaneously and independently of one another. Calculate

(a) the probability of the first roll being a 1, given that the sum of both rolls was 5,

(b) the probability of the sum being 5, given that the first roll was a 1 and

(c) the probability of the first roll being a 1 and the sum being 5.

Finally,

(d) verify your results with Bayes’ theorem.