A , B , and C are three events such that P ( A )=0.6 , P ( B )=0.4, P ( C )=0.5, P ( A B )=0.8, P ( A C )=0.3 and P ( A B C )=0.2 and P ( A B C ) 0.85 . What is the minimum value of P ( B C ) ?

Step-by-step solution

aligned P ( ~A )=0.6, P ( ~B ) & =0.4, P ( C )=0.5 P ( ~A ~B ) & = P ( ~A )+ P ( ~B )- P ( ~A ~B ) & =0.6+0.4-0.8=0.2 aligned Now, aligned P ( ~A ~B C )= & P ( ~A )+ P ( ~B )+ P ( C ) & - P ( ~A ~B )- P ( ~A C ) & - P ( ~B C )+ P ( ~A ~B C ) = & 1.5-0.2-0.3- P ( ~B C )+0.2 aligned array rlrl & P ( A B C ) & =1.2- P ( B C ) & 0.85 & P ( A B C ) 1 & 0.85 & 1.2- P ( B C ) 1 & -0.35 & - P ( B C ) -0.2 & 0.2 & P ( B C ) 0.35 array Minimum value of P ( B C )=0.2 .