Probability of X>y =p1 y>z = p2 z>x =p3 ,find minimum of P1 +p2 +p3…

X,Y and Z are 3 random variables such that

Probability of X>Y=p1,Y>Z=p2,Z>X=p3

a) thus find maximum of p1+p2+p3

b) what is the maximum that minimum value of p1,p2 and p3 may take?

Hint is provided as : consider set theory operation.

My thinking process - let us define the events X>Y =A, Y>Z =B, Z>X =C

Now P(AUBUC) = p1 + p2 + p3 -p1p2 -p2p3 -p3p1 + 0

now P(AUBUC) is at most 1 therefore i have the inequality ==> p1 + p2 + p3 <= p1p2 +p2p3 +p3p1 + 1

i don't know how to proceed further! maybe some geometric figures .etc etc !

thanks!