Suppose 10% of the people are good at art, and that 40% of the people who are good at art are also good at math. If a person is not good at art, they have only a 30% chance of being good at math. What is the probability that a person who is good at math will also be good at art?
Is my solution correct?:
Let M be person being good at math and A be good at art. Then A’ is being not good at art
P(A)=0.1
P(M|A)= 0.4
P(M|A’)=0.3
So P(M)=0.4+0.3=0.7
By bayes theorem: P(A|M)=0.4*0.1/0.7=0.06
Sometimes a figure is worth 1000 words:
So consider just the "good at math" area. What proportion of that is also "good at art"?