A shopkeeper keeps two cartons of glass marbles. Carton A holds 5 white and 3 red marbles; carton B holds 3 white and 7 red marbles. One marble is drawn at random from each carton. What is the probability that at least one of the two marbles drawn is red?

Work through the complement. 'No red at all' needs white from A and white from B, and the two draws are independent: (5/8) × (3/10) = 15/80 = 3/16. Hence P(at least one red) = 1 − 3/16 = 13/16. Trap 3/16 is that complement left unsubtracted — the commonest slip in 'at least one' questions. Trap 21/80 = (3/8) × (7/10) is 'both red', a much stricter demand. Trap 1/2 guesses without using either carton.