I’m working on a lane with no walkway, and need to know the probability that a pedestrian will come across a car.

I have attached my spreadsheet in this Dropbox link.

https://www.dropbox.com/s/2kf7agr86l5m3ev/Probability of Car meeting Pedestrian.xlsx?dl=0
Explanation is below.

Worst Case - Evenly Spaced
If all cars and peds were evenly spaced, then the probability of a car on that road during an hour is 100% (60mins/30cars = 2mins/car, 2mins/car<3min to travel) similarly for the peds. So 100% chance a ped will come across a car.

Best case - single group
If all cars were in 1 group (assume side by side for simplicity), then it would take the cars 3 minutes to drive on that road, or 5% of the hour (3mins/60mins)

And peds 12 minutes to walk, or 20% of the hour (12mins/60mins).

So the probability that they meet is 5% x 20% =1%.

Average
The result above cover a massive range and not ideal when presenting. So I want a mid-point and this isn’t simply finding the middle of these probabilities.

I approached it like this,

Car:

The max number of groups of cars per hour to equal the 3 min travel time is 20 (60mins/3mins).

This is 66.7% of the total 30 cars.

So if there are 20 groups or more, a car will 100% be on the lane at any time in that hour.

As for below 20 groups, I have simply found assumed on average this will be 10 groups (50% of 20 groups).

So 100%*33.3% + 50%*66.7% = 66.7% of a car on this lane at any point in the hour.

Peds:

Do the same approach for peds, and this results in 87.5%.

66.7%*87.5% = 58.3% of a pedestrian and car meeting on a lane.

Please let me know what you think.

Thanks