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Bayes' theorem Reading 8 Schweser Comprehensive Prob #3

My question is regarding the answer that appears for this problem. The book says the answer is calclulated by: 30% / 51.25% = 58.25%.
However, according to Bayes’ theorem:
P(I|O)= [ P(O|I) / P(O) ] x P(I)
So, why don’t they later multiply the 58.25% above by the 75% that is the probabilitiy of Score >= 20?
Thanks for your help guys.

don’t even bother with that equation. learn with the tree. it’s outlined in schweser.

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You’re right. With the formula I had confused the conditional probability with the joint prob. so there was no need to multiply again by 75% because the 30% was already 75% times 40%. With the tree it’s easier not to get confused.
Thanks.

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