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

Algebra ->  Probability-and-statistics -> 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      Log On


   

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(52776) About Me  (Show Source):
You can put this solution on YOUR website!
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(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

         3%2F4 = 1%2F2 + 2%2F3 - P(A and B).


     It gives you

          P(A and B) = 1%2F2+%2B+2%2F3+-+3%2F4 = 6%2F12+%2B+8%2F12+-+9%2F12 = %286%2B8-9%29%2F12 = 5%2F12.     ANSWER



(ii)  The given equality  P(A|B) = 2%2F5  means, by the definition of the conditional probability, that

          P(A and B)/P(B) = 2%2F5.


      It implies that

           P(A and B) = %282%2F5%29%2AP%28B%29 = %282%2F5%29%2A%282%2F3%29 = 4%2F15.     ANSWER


      Notice that the given value  P(A) = 1%2F2  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
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