If P(A B)= 5 6 , P(A B)= 1 3 and P( not A)= 1 2 , then which one of the following is not correct?

Step-by-step solution

aligned & P(A B)= 5 6 , P(A B)= 1 3 , P (A^ )= 1 2 & P(A)=1-P (A^ )=1- 1 2 = 1 2 & P(A B)=P(A)+P(B)-P(A B) aligned 5 6 = 1 2 +P(B)- 1 3 (a) P(B)= 5 6 - 1 2 + 1 3 = 5-3+2 6 = 4 6 = 2 3 (b) P(A B)= 1 3 = 1 2 2 3 =P(A) P(B) P(A B)=P(A) P(B) (c) P(A B)= 5 6 aligned & P(A)+P(B)= 1 2 + 2 3 = 7 6 & P(A B) P(A)+P(B) aligned Hence, option (c) is not correct. (d) P (A^ B^ )=P (A^ ) P (B^ ) aligned & 1-P(A B)=1- 5 6 = 1 6 & and P (A^ ) P (B^ )=(1-P(A)) (1-P(B)) & = (1- 1 2 ) (1- 2 3 )= 1 2 1 3 = 1 6 aligned Hence, P (A^ B^ )=