If A and B are two events such that P(A B)=0.1 , and P(A B) and P(B A) are the roots of the equation 12 x^2-7 x+1=0 , then the value of P ( A B ) P ( A B ) is :

Step-by-step solution

P(A B)=0.1, P(A B) and P(B A) are the roots of the equation 12 x^2-7 x+1=0 aligned & P(A B) P(B A)= 1 12 & P(A B) P(B) P(A B) P(A) = 1 12 & P(A) P(B)=12(0.1)^2 & =0.12 aligned Also, P(A B)+P(B A)= 7 12 aligned & P(A B) ( 1 P(B) + 1 P(A) )= 7 12 & P(A)+P(B)= 7 12 0.12 0.1 & P(A)+P(B)=0.7 & P( A B ) P( A B ) = P( A B ) P( A U B ) & = 1-P(A B) 1-P(A B) & = 1-0.1 1-(0.7-0.1) = 0.9 0.4 = 9 4 aligned