Question

Main Street in Middletown runs north-south a total of ten blocks, with a restaurant at each end: Ani's Taqueria on the north end and Ramen House at the south end. You're standing in the middle, five blocks from each, and are in need of a meal You can't decide which way to go, so you decide to leave it up to the fates. Specifically, you decide that you'll roll one die; if it comes up between 1" and "4," then you'll walk one block north, and if it comes up "5" or "6," you'll walk one block south. You repeat this until you arrive at one or the other restaurant. What are the odds that you'll wind up at the Ramen House? Choose the best answer. g92 1,023 31 1,023 1,023 31 X

Answer 1

This is an example similar to the Gambler's ruin problem.

Let Pn be the probability that the person goes North, and Ps be the probability that the person goes South.

Let South be 0 and North be 10. We start at point 5.

Thus, i=5 and N=10.

Probability of success (going North),p is 4/6 or 2/3.

Probability of going South,q is 2/6 or 1/3.

P(ending up North)= [1-(q/p)ⁱ ] / [1-(q/p)^N ]

= [1-(1/2)⁵ ] / [1-(1/2)¹⁰ ]

= 992/1023

P(ending up South)= 1- p(ending up North)

= 1- 992/1023

= 31 / 1023

Odds(ending up South)= 31/1023 / 992/1023

= 31/992 or 1/32

We have been asked to choose the best answer. The best answer from the given options is 31/1023.