I can't figure this out. Help appreciated.
A box contains four balls, numbered 1 through 4. One ball is selected at random from this box.
Let X1=1 if ball number 1 or ball number 2 is drawn.
Let X2=1 if ball number 1 or ball number 3 is drawn.
Let X3=1 if ball number 1 or ball number 4 is drawn.
The Xi values are zero otherwise. Show that any two of the random variables X1, X2, X3 are independent but that the three together are not.
I could really use some help. Thank you.