[Probability] – A tree diagram problem
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?