Thread: [Probability] – A tree diagram problem

1. [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?

2. Originally Posted by geton
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?
Your tree diagram is correct. Where are you stuck using it? For (b), use it to find the combination that has the largest probability.

3. Originally Posted by mr fantastic
Your tree diagram is correct. Where are you stuck using it? For (b), use it to find the combination that has the largest probability.
Thanks I got it.