Find the probability that the person
1. is Young, given that the person drinks diet cola.
2. drinks diet cola, given that the person is Young.
+1667 No, these questions are not the same.
Let us assume that 150 people were surveyed, and the results were that 80 are young, 70 are old, 72 drink diet cola, and 78 do not.
So, out of the people that drink diet cola, let's say only 54 out of the 72 are young....
And so out of the people that are young, those 54 out of the 80 young people drink diet cola.
This means that the hypothetical probability for a person being young, given that they drink diet cola, is 54/72, while the probability for a person drinking diet cola, given that they are young, is 54/80.
These probabilities are different, and while rarely the questions can result in the same answers, they are definitely not the same, and usually do not lead to the same probability.
