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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

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  • $\begingroup$ What have you tried ? where are you stuck ? It's not a homework service : How to ask a good question. $\endgroup$
    – Surb
    Dec 23 '20 at 18:40
  • $\begingroup$ @Surb oh sorry ill edit in my solution $\endgroup$
    – eipim1
    Dec 23 '20 at 18:40
  • $\begingroup$ 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. $\endgroup$ Dec 23 '20 at 19:27
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Sometimes a figure is worth 1000 words:

enter image description here

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

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  • $\begingroup$ Im getting 4/31 for this. Hmm makes sense $\endgroup$
    – eipim1
    Dec 23 '20 at 22:05
  • $\begingroup$ Then maybe a $\checkmark$ (or at minimum +1) is in order. $\endgroup$ Dec 23 '20 at 22:29
  • $\begingroup$ Nice answer. (+1) $\endgroup$
    – BruceET
    Dec 24 '20 at 2:41

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