# Question regarding conditional probabilities

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

• What have you tried ? where are you stuck ? It's not a homework service : How to ask a good question.
– Surb
Dec 23 '20 at 18:40
• @Surb oh sorry ill edit in my solution Dec 23 '20 at 18:40
• Your answer is not correct. Drawing a probability tree will solve your question. You may aslo assume that there are 100 people in total and create a 2 by 2 table to help you understand the question. Dec 23 '20 at 19:27

Sometimes a figure is worth 1000 words:

So consider just the "good at math" area. What proportion of that is also "good at art"?

• Im getting 4/31 for this. Hmm makes sense Dec 23 '20 at 22:05
• Then maybe a $\checkmark$ (or at minimum +1) is in order. Dec 23 '20 at 22:29
• Nice answer. (+1) Dec 24 '20 at 2:41