Category: Hobbies

A Probability Surprise

For quite a while now I’ve been exercising on a regular basis. My favourite physiotherapist recently told me there was a fair bit of overlap in the exercises I was doing. I had multiple exercises that were working the same muscles. In these cases he suggested I could either just pick one of the two, or alternate between them.

I’m slightly embarrassed to admit that I get a bit excited when I stumble across a real life situation that gives me the (contrived?) opportunity to tell myself “I can build an app for that!”

Specifically, I started out wanting to build an app that would:

have the details of all the exercises I use
know which ones could be alternated
generate a ‘random’ program that would select among the pairs of exercises that were interchangeable.

But then I thought of a couple of things that caused me to increase the scope of the project.

I wanted to be able to specify the relative probabilities in a pair of exercises (for example pick one 65% of the time and pick the other 35% of the time)
I wanted to be able to choose 2 exercises out of a group of 4 and have it randomly pick different pairs.

For example, I have 4 calf exercises, and I wanted to randomly pick 2 each time I was working out. So if I weighted all 4 equally and picked 2 each one would be included 50% of the time. But if I weight one at 50% and the other 3 at 16.67%, when I choose 2, how frequently would the 50% exercise be selected?

SideNote: Why does it matter what fraction of the time an exercise gets picked? In terms of building the app, it doesn’t really matter. My main motivation for figuring out how to calculate this was to make sure that the random selection code was working correctly.

In the case where the app picks 2 items from a set of four individually weighted choices, how could I determine how frequently each item would get picked.

list all the possible combinations [(1,2), (1,3), (1,4), (2,1), (2,3), (2 ,4), (3,1), (3,2), (3 ,4), (4,1), (4,2), (4,3)]
determine the probability of each combination. Note that the probability calculations for the second selection need to exclude the item that was picked first. For example, using the previous values (50%, 16.67%, 16.67%, 16.67%) when 1 is picked first, the probabilities for 2,3,4 will all be 33%. When 2 is picked first, the probabilities for 1,3,4 will be 60%, 20%, 20%
for each combination in step 1, multiply the probabilities for the first pick and the second pick, to determine the probability of each combination. Note in the current example
(1,2) => (50% x 33.33%) => 16.67% but
(2,1) => (16.67% x 60%) => 10%
make sure the sum of all the probabilities is 100%
sum the probabilities for all the combinations that include the item in question. For example, item 2’s list of combinations would be [(1,2), (2,1), (2,3), (2 ,4), (3,2), (4,2)]

But here’s the part that was counterintuitive (at least to me): When I change the relative weighting of item 1 and item 2, the probailities for item 3 and item 4 will change. (even though their weightings stay exactly the same.

In the 4 choose 2 example, when all 4 items are weighted equally, all items will appear in 50% of the results. But when item 1 is reduced to 5% and item 2 is increased to 45% (items 3 and 4 are both left at 25%) item 3 and item 4 will now appear in 55% of results.

Tags Probability

Hobbies Photography

Focus!

Post author By root
Post date October 9, 2025
No Comments on Focus!

Several months ago, I took my beloved favourite camera to a Hana soccer game, fully intending to take photos. Between the torrential rain, and my parents having come to watch I ended up not taking any photos. My camera stayed in my pack for the entire game. Sadly I hadn’t paid much attention to protecting it from the rain. (spoiler: wrapping a camera in a tattered plastic shopping bag, and putting it in an entry level day pack will lead to heartbreak if you stand in the rain for 2 hours.)

After the game ended I took a few of photos and they were all out of focus. I didn’t think much of it, but the next time I took soccer photos, they were all unsharp. And the time after that, more blurry photos. Time to take my head out of the sand. After trying multiple lenses on both camera bodies, I became reasonably confident both the body and the lens had issues.

I sent the body to Nikon (something I hate doing) but was still unsure what I should do about the lens. I’d bought some time waiting until the body came back, but soon would need to figure out how to ‘fix’ the lens. (My camera body is a Nikon D500 and the lens is an 80-200 AF 2.8)

When my body came back from Nikon, I wanted to figure out how to get my favourite lens back to being useful. My first plan was to setup my fancy test target try different AF-FineTune values. I eventually landed on the following setup:

test target in the bright sun shine
camera mounted on a tripod close enough that the target filled the frame (but far enough away that it could focus)
shutter release timer

I forget the exact AF FineTune value that resulted from this exercise, but sadly when using the lens wide open, it still tended to focus behind the subject. 🙁

I was able to sort of work around this by:

trying to focus in front of my subjects
stopping down the aperture (eg F4)

But still, even with these adaptations I was getting a large portion of photos being blurry. Eventually, I tried a different experiment. I:

took my son’s bike to a grassy field and set up the camera on a tripod 20 feet away
set the zoom to 80mm (widest value)
using typical settings (1/1000s, f2.8) took photos using different AF Fine Tune values (-20, -15, -10, -5, 0, 5, 10, 15, 20)
Moved the camera a few different distances from the bike (35′, 45′, 70′) For the middle distances, I used multiple zoom values (typically 80mm, 125mm, 200mm) The further away I went, the longer the focal lengths I used.
In all distance/focalLength combinations, I’d take photos with the same array of AF Fine Tune values

The results of this experiment were revealing. All photos were focused behind the bike. The -20 photos were generally less back focused, not much too blurry to be usable.

Unfortunately, the cost of repairing this lens most likely exceeds the cost of replacing it.

In happier news I have now acquired a very modern 70-200 F4 lens. Less shallow depth of field, but also less weight, and much less expensive. While I still dream of switching to mirrorless (I’d love to use a Z6iii) I’m enjoying the sharp photos I’m able to create with my 70-200 and D500. I’ve also enjoyed doing the ‘bike on grass’ experiment with different combinations of lens and body.