Q. 245.0( 5 Votes )

If A and B are tw

Answer :

Basic Idea: If A and B are two independent events then


P(A B) = P(A)P(B) and A’ and B or B’ and A are also independent and same logic can be applied to them.


Let P(A) = x and P(B) = y


P(A’) = 1 – x and P(B’) = 1 – y


Given that,


A and B are independent. So,


P(A’ B) = P(A’)P(B) = 2/15


(1-x)y = 2/15 …(1)


Similarly, P(A B’) = P(A)P(B’) = 1/6


x(1-y) = 1/6 …(2)


From equation 1 and 2 we can write as-







180x2 + 30 = 186x


180x2 – 186x + 30 = 0




also x =


P(A) =


Putting x = in equation 1,we get


y =


Hence,


P(A) = 1/5, 5/6


Or P(B) = 1/6, 4/5


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