aez-notes

Coupons in cereal boxes are numbered \(1\) to \(5\), and a set of one of each is required for a prize. With one coupon per box, how many boxes on the average are required to make a complete set?

The first coupon comes in the first box, then each new one follows after a geometric number of boxes. We need to be careful because the geometric distribution in the distrib package starts at zero.

load(distrib);

mean_geometric(1);

prob_new_coupon : [5/5,4/5,3/5,2/5,1/5];

mean_boxes(p) := mean_geometric(p) + 1;

mean_total_boxes : apply(
  "+",
  map(mean_boxes, prob_new_coupon)
);

/* approximately 11.42 */