SOLUTION: Let P(E) = 0.35, P(F) = 0.3, and P(E ∩ F) = 0.15. Draw a Venn diagram and find the conditional probabilities. (a) P(F | E ∩ F) (b) P(EC | E )

Algebra ->  Probability-and-statistics -> SOLUTION: Let P(E) = 0.35, P(F) = 0.3, and P(E ∩ F) = 0.15. Draw a Venn diagram and find the conditional probabilities. (a) P(F | E ∩ F) (b) P(EC | E )      Log On


   

Question 1125792: Let P(E) = 0.35, P(F) = 0.3, and P(E ∩ F) = 0.15. Draw a Venn diagram and find the conditional probabilities.

(a) P(F | E ∩ F)


(b) P(EC | E )
Answer by ikleyn(52786) About Me  (Show Source):
You can put this solution on YOUR website!
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Let P(E) = 0.35, P(F) = 0.3, and P(E ∩ F) = 0.15. Draw a Venn diagram and find the conditional probabilities. 


    (a)  P(F | E ∩ F) = P(F ∩ E)/P(E ∩ F) = 0.15+%2F+0.15 = 1.
 
 

    (b)  P(EC | E ) = P(EC ∩ E)/P(E) = 0%2FP%28E%29 = 0.


You do not need Venn diagram to solve this problem.

All you need is to know the basic definitions.