Draw the three bars one at a time. Each A_n contains the one before. The readout on the right is P(A_n) = 1 - e^{-n}.
Let them predict first.
The new piece of A_3 is {2 < X <= 3}: B_1, B_2, B_3 do not overlap, and together they rebuild the same union.
The density is e^{-x}. Each new piece B_n owns the slice of area between n-1 and n.
Let them predict first.
Matching middle terms cancel in pairs: only 1 and -e^{-k} survive, so the partial sum is 1 - e^{-k} = P(A_k).
Same pieces, second route: P(B_n) is geometric with ratio e^{-1}.
Structure only. Each box is one move; the homework asks you to carry them out for any increasing events.
Left: numbers only, as in the guide. Right: the five-step recipe. Then do the drills by hand.