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This pertains to the following post:

When to use Total Probability Rule and Bayes' Theorem.

I understand the ideas and can implement them if I'm told what B and the partitions A are in the question - or that i'm meant to use the law of total prob - but always get stuck in these type of questions if I don't know specifically what method I'm meant to use. I get the venn diagrams below but can never work out from the questions what should be B and what the partitions A_1, A_2, etc represent.

Any tips would be great.

total prob 1

total prob 2

jm007
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  • I'd suggest just thinking intuitively about the given problem and trying to build a Venn-diagram-like mental picture of the situation. Basic properties of probabilities like Bayes' rule are sort of self-evident if you think about them the right way, so you can usually figure out the right approach if you identify the relevant quantities and think about how they ought to be related to each other instead of worrying about which rule to apply. Seeing lots of examples also helps build this intuition. – Karl Jul 16 '23 at 07:26

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