A point is chosen from the lattice points in the first quadr

A point is chosen from the lattice points in the first quadrant. The sample space for this random experiment is Ω={(i, j) : i, j E {0,1,2...}}. Assign the outcome (i,j) probability e-52i3j/i!j!
a. show that the probability assignment is legitimate
Find the probability that the point selected
b. is on the x-axis
c. is in the closed square of side length 3 with lower left vertex at the origin
d. has x coordinate i, where i is a nonnegative integer
e. has y coordinate j, where j is a nonnegative integer