The probability of simultaneous occurrence of atleast one of two events A and B is p . If the probability that exactly one of A, B occurs is q then P (A^ )+P (B^ ) is equal to

Step-by-step solution

Since, P( exactly one of A, B occurs )=q . P(A B)-P(A B)=q p-P(A B)=q P(A B)=p-q 1-P (A^ B^ )=p-q P (A^ B^ )=1-p+q P (A^ )+P (B^ )-P (A^ B^ )=1-p+q P (A^ )+P (B^ )=(1-p+q)+[1-P(A B)]=(1-p+q)+(1-p)=2-2 p+q