# Thread: Help with Pathway Probability Problem

1. ## Help with Pathway Probability Problem

I am completely lost on how to solve this problem. Any hint would help

There is a lost tourist in New York. The streets in New York run east to west and go from

..., S. 2nd St., S. 1st St., Broadway St., N. 1st St., N. 2nd St., ...
The avenues run north to south and go from

..., E. 2nd Ave., E. 1st Ave., Broadway Ave., W. 1st Ave., W. 2nd Ave., ...
These streets form a square block grid. For each of the questions below, the tourist starts at the intersection of Broadway St. and Broadway Avenue and moves one block in each of the four cardinal directions with equal probability.

What is the probability that the tourist is at least 3 city blocks (as the crow flies) from Broadway and Broadway after 10 moves?

What is the probability that the tourist is at least 10 city blocks (as the crow flies) from Broadway and Broadway after 60 moves?

What is the probability that the tourist is ever at least 5 city blocks (as the crow flies) from Broadway and Broadway within 10 moves?

What is the probability that the tourist is ever at least 10 city blocks (as the crow flies) from Broadway and Broadway within 60 moves?

What is the probability that the tourist is ever east of East 1st Avenue but ends up west of West 1st Avenue in 10 moves?

What is the probability that the tourist is ever east of East 1st Avenue but ends up west of West 1st Avenue in 30 moves?

What is the average number of moves until the first time the tourist is at least 10 city blocks (as the crow flies) from Broadway and Broadway.

What is the average number of moves until the first time the tourist is at least 60 city blocks (as the crow flies) from Broadway and Broadway.

2. ## Re: Help with Pathway Probability Problem

Hi! We are glad that you posted here! This looks like a homework question though. Our homework help policy can be found here. We mainly just want to see what you have tried so far and that you have put some effort into the problem. I would also suggest checking out this thread for some guidelines on smart posting behavior that can help you get answers that are better much more quickly.

 Tweet

#### Posting Permissions

• You may not post new threads
• You may not post replies
• You may not post attachments
• You may not edit your posts