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Ask Marilyn: Is This Drawing Fair?
Frankie St. Phillips of Anderson, Indiana, writes:
Marilyn: Our organization of 250 members has a drawing using three jugs to determine the winner. Everyone is assigned a number from 000 to 249. The first jug contains three ping pong balls numbered 0, 1, and 2. The second and third jugs each contain balls numbered from 0 through 9. If a number from 250 through 299 is drawn, the drawing is repeated.
When a 2 is drawn from the first jug, do people with a number from 000 to 199 have the same chance of winning as people with a number from 200 through 249? The outcomes of the drawings are different. Drawings from 000 to 199 are not repeated. But if a 2 is drawn from the first jug, everybody gets a second chance when a number over 249 is drawn.
All members have the same chance of winning. Envision the drawing this way: All three numbers (one from each jug) are drawn at the same time. If someone wins, the drawing is over. If no one wins, the drawing is repeated. Lengthening the process by drawing a ball from the first jug, then the second one, and then the third jug doesn't change this. It just adds to the suspense.