Question

Mike determined that some children like to eat cake, some like to eat cookies, and others don't like to eat cake or cookies. He calculated the probabilities and created the Venn diagram below:
a venn diagram showing two categories, cake and cookies. In the cake only circle is 0.2 in the cookies only circle is 0.5, in the intersection is 0.1, outside the circles is 0.2

What is the probability that a child eats cake, given that he/she eats cookies?

Answer 1

Hey there!

This is an example of conditional probability, or P(A | B). Let's say that the probability of a child eating cake is event A, and the probability of them eating cookies is event B. 

Conditional probability (A, given that B has occurred) can be represented and found by the following equation:

P(A | B) = P(A ∩ B)/P(B)

P(A ∩ B) is the probability of a child eating both cake and a cookie. This is also the middle of the venn diagram you were given. P(B) is simply the probability of event B happening, which, as we established, is eating a cookie. 

P(A | B) = P(A ∩ B) / P(B)
P(A | B) = 0.1 / 0.5
P(A | B) = 0.2

There will be a 0.2, or 20%, chance that a child will eat cake, given that they've eaten a cookie. 

Sorry for the late response, but I hope this still helped you out!