SOLUTION: Find P(A and B) if; (i) P(A)=1/2, P (B)=2/3, P(A or B)=3/4 (ii) P(A)=1/2 P(B) =2/3, P(A|B)=2/5

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Question 1163268: Find P(A and B) if;
(i) P(A)=1/2, P (B)=2/3, P(A or B)=3/4
(ii) P(A)=1/2 P(B) =2/3, P(A|B)=2/5
Answer by ikleyn(52780)   (Show Source): You can put this solution on YOUR website!
.

(i)  Use the general formula of the Probability theory

         P(A or B) = P(A) + P(B) - P(A and B).


     Substitute the given data to the formula

          =  +  - P(A and B).


     It gives you

          P(A and B) =  =  =  = .     ANSWER



(ii)  The given equality  P(A|B) =   means, by the definition of the conditional probability, that

          P(A and B)/P(B) = .


      It implies that

           P(A and B) =  =  = .     ANSWER


      Notice that the given value  P(A) =   is IRRELEVANT to the solution of the part (ii).

Solved.

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If you want to see many other similar solved problems, look into the lessons
    - Elementary operations on sets help solving Probability problems
    - Elementary operations on sets help solving Probability problems - REVISITED
    - Using general probability formulas for a union or intersection of events
    - Conditional probability problems
in this site.



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