Discussion Board 8

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Description:

Students will read a scenario about probability and discuss their thoughts on answers given, as well as answer the question themselves.

Objectives:

• Students will find the probability of on an event how it changes.

Instructions:

Step 1: Respond to the following:

• Read the following scenario and responses. Respond to the original question of "When would you take your turn?" and give your reasoning.

Ask Marilyn Parade Magazine, 3 January 1999, p. 16 Marilyn vos Savant

In an earlier column (Parade, 29 November 1998, p. 26) Marilyn responded to the following question:

You're at a party with 199 other guests when robbers break in and announce they're going to rob one of you. They put 199 blank pieces of paper in a hat, plus one marked "you lose." Each guest must draw a piece, and the person who draws "you lose" gets robbed. The robbers think you're cute, so they offer you the option of drawing first, last or any time in between. When would you take your turn?

Marilyn said she would choose to draw first, explaining that "It would make no difference to my chances of losing--any turn is the same--but at least I'd get to leave this party as soon as possible." Not all of her readers agreed, and the present column contains responses from some of them.

One letter argues for drawing first: "You said any turn is the same, but I believe that would be true only if the partygoers all had to replace the papers they drew before another selection was made. But if they keep the papers (the scenario intended by the question), wouldn't the odds of losing increase as more blanks were drawn? If so, drawing first is best."

Another reader argued for drawing last: "Though you have a 1-in-200 chance of getting a blank paper and not being robbed if you go first, the odds are 199 in 200 that the drawing will end with a loser (other than you) before you draw if you go last. You should go last."

Marilyn restates her original position that it makes no difference where in the process you draw. She argues that the answer would be the same as if everyone drew simultaneously, in which case it would be more intuitive that everyone has the same 1-in-200 chance. She offers another argument based on people buying tickets for a church raffle, explaining that it makes no difference whether you buy your ticket immediately when you arrive or wait until just before the drawing.