A certain statistician’s breakfast consists of either some cereal or toast (but not both) to eat and one drink from a choice of fruit juice, tea or coffee. If he has cereal to eat, the probability that he chooses coffee is 3/5 and the probability he chooses tea is 3/10. If he has toast to eat, the probability he chooses coffee is 2/5 and the probability he chooses tea is 1/5.

Given that he has cereal with probability ¾.

(a) find the probability that on any particular day he has

(i) fruit juice (ii) cereal & coffee.

(b) Find his most popular breakfast combination.

I draw a tree diagram like this.

Is it right? If wrong then how could I draw this?

Then now what to do?