Today's study group.   Example of the union bound.

X is a continuous random variable, thus
P(X = 3) = 0
P(X = n) = 0
and we do not have to weary about boundaries.

P(A1) = P[0 <=  X <= 2]  = 1/(2^2)
P(A2) = P[1 <=  X <= 3]  = 1/(2^3)
P(A3) = P[2 <=  X <= 4]  = 1/(2^4)
.............................

by the union bound:
P(union Ai)  <=  1/(2^2) + 1/(2^3) + 1/(2^4) +...