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To start off, I've been reading "Statistics: Principles and Methods" 7th edition by Johnson and Bhattacharyya. I understand the conditional probability formulas and have practiced the examples in the book. What I do not understand is how to apply this to a pair of stocks. For example, let's say stock A going up 2% has a .08 probability, and stock B going up 3% has a .06 probability. What is the conditional probability of stock A going up 2% given that stock B went up 3%?

Here is my guess which I believe is incorrect. P(A|B) = P(AB)/P(B). So (.08+.06)/.06 = 2.33%. Is that right or wrong? Thank you for reading.

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You cannot say anything by only knowing the marginal probabilities of stock increase in companies A and B respectively. You need some statement about the joint or conditional probability, e.g. prob A increases given B increases or prob A and B increase together. These allow you to apply Bayes rule for calculating other conditional probabilities in the problem.

To make this easier to understand, always be sure to check whether the description of the problem, such as yours, allows for independence or complete determination. Stock B's movement may not change probabilistically based on Stock A's performance. Alternately, Stock B may be practically identical to Stock A.

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  • $\begingroup$ So are you saying I should use Bayes' Theorem? P(B|A)=P(A|B)P(B) / P(A|B)P(B)+P(A|Bc)P(Bc) where c is complement? $\endgroup$
    – kits
    Jul 8 '15 at 21:53

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