what you have to do is to define the probabilities of all the events:
P(X1) = 1/2 , because X1 will occur ( be 1 ) when the ball will have numbers 1 or 3 out of 4 options, meaning 2/4.
in the same way:
now you have to look at the intersections:
P(X1 and X2 ) = 1/4 (why ? ), and also P(X1)*P(X2)=1/4, so X1 and X2 are independent.
do the same for X1 & X3, X2 & X3.
the probability of all Xi to occur is 1/4, while P(X1)*P(X2)*P(X3)=1/8, so all the events are not independent.
you say that the 3 events are pairwise independent.