Weihnachtsmann rot

Challenge from 12. December

Frog and Toad

The weekend challenges can be solved without wasting points until Monday 11:59:59pm (CET). For more information see the rules of the game.

Enjoy the puzzle!

Authors: , Jesper Nederlof

Project: 4TU.AMI

Challenge:

The probability frog Frederick jumps around on the integers. At 8 am, he starts on the number +100 and makes a jump every second. Fredrick prefers to jump to the left (to the smaller numbers) than to the right (to the larger numbers): with probability 1/3 he jumps from his current position f to f+1, with probability 2/3 he jumps to f-1. In the course of the day, Frederick reaches the number 0 and ends his journey.

The probability toad Topanga also jumps around on the integers. At 8 am she starts on the number -100 and makes a jump every second. Just like Frederick, Topanga prefers to jump to the left rather than to the right: with probability 1/3 she jumps from her current position k to k+1 respectively, with probability 2/3 she jumps to k-1. In the course of the day (but not in the same second as Frederick) Topanga reaches the number 0 and ends her journey.

With p we denote the probability that Frederick reached the number 0 only after Topanga.

Which of the following statements about p is true?

Artwork: Julia Nurit Schönnagel

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Possible answers:

  1. p ≤ 0.002 holds.

  2. 0.002 < p ≤ 0.004 holds.

  3. 0.004 < p ≤ 0.008 holds.

  4. 0.008 < p ≤ 0.016 holds.

  5. 0.016 < p ≤ 0.032 holds.

  6. 0.032 < p ≤ 0.064 holds.

  7. 0.064 < p ≤ 0.128 holds.

  8. 0.128 < p ≤ 0.256 holds.

  9. 0.256 < p ≤ 0.512 holds.

  10. 0.512 < p holds.

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