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I need some help solving this problem.

A man is about to perform a random walk. He is standing a distance of 100 units from a wall. In his pocket, he has 10 playing cards: 5 red and 5 black.

He shuffles the cards and draws the top card.

If he draws a red card, he moves 50 units (half the distance from the wall) to the right (away from the wall).

If he draws a black card, he moves 50 units (half the distance from the wall) to the left (towards the wall).

How far from the wall will he be after all 10 cards have been drawn?

Thank you in advance for your help!

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    Thanks for your questions and answers. He moves$50$units each time he draws a card. Once he hits the wall, he stays put but keeps drawing cards until all 10 cards are drawn.2012-04-14

2 Answers 2

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Hint: The ending position is independent of the order the cards are drawn (Prove this). What happens if you have only one of each?

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HINT: If he always moves half the current distance to the wall, his distance from the wall is multiplied either by $\frac12$ or by $\frac32$ each times.