Need help with Probability and Statistics

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A and B are events with Pr[A] = 0.25, Pr[B] = 0.32, and Pr[A ∩ B] = 0.06.

Calculate .

Mar 30th, 2015

I  assumed B' means the complement of B. 
A is the union of the two disjoint events A ∩ B', A ∩ B and so 
Pr[A] = Pr[A ∩ B'] + Pr[A ∩ B]. 

Pr[A|B'] = Pr[A ∩ B'] / Pr[B'], from the definition of conditional probability 
= (Pr[A] - Pr[A ∩ B]) / (1 - Pr[B]), since Pr[A] = Pr[A ∩ B'] + Pr[A ∩ B] 
= (0.25 - 0.06) / (1 - 0.32) 
= 0.19/0.68 
= 19/68 

= 0.2794 

by multiplying with 100% we get
 = 27.94%

Mar 30th, 2015

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