`P(A)=p , P(B)=2p , P("exactly one out of A and B occurs")=5/9` then what will be maximum value of p ?

If A and B are independent events such that P(A)=p ,\ P(B)=2p\ a n d\ P (Exactly one of A and B occurs ) =5/9 , find the value of pdot

If E and F are independent events with P(E)=p and P(F)=2p and P( exactly one of E,F)=(5)/(6) then find the value of p

For the three events A, B and C, P(exactly one of the events A or B occurs) = P(exactly one of the events B or C occurs) =P(exactly one of the events C or A occurs)= p and P(all the three events occur simultaneously) = p^2, where 0ltplt1/2. Then, find the probability of occurrence of at least one of the events A, B and C.

For three events A, B and C, P (Exactly one of A or B occurs) = P (Exactly one of B or C occurs) = P (Exactly one of C or A occurs) = (1)/(4) and P(All the three events occurs simultaneously = (1)/(16) . Then the probability that at least one of the events occurs, is :

For the three events A ,B ,a n dC ,P (exactly one of the events AorB occurs)=P (exactly one of the two evens BorC )=P (exactly one of the events CorA occurs)=pa n dP (all the three events occur simultaneously)=p^2w h e r eo