This was a very fun story to go through! I wonder if this format could be used as an effective way of structuring lessons in school. Each juncture that requires a choice to be made would (ideally) encourage class participation and debate. After a period of discussion, a vote would be taken, a decision would then be made, and the next section of the lesson would begin.
I'm not a teacher, and I know from friends who are that being a good teacher is harder than what I can probably imagine, but I think kids would have fun working through these types of stories.
[edit; whoops you were talking about the format and I was talking about the material. Oh well, hopefully this is not too out of place.]
It could be made much more approachable by removing the math entirely. If you learned programming before algebra you might have solved it like this:
from random import random
from collections import defaultdict
tally = defaultdict(int)
for i in range(100000):
thief = ['raccoon', 'fox'][random() < 0.3]
bear = ['false', 'true'][random() < 0.8]
hair = ['raccoon', 'fox'][random() < 0.3333333]
if thief == 'raccoon' and bear == 'true':
continue
if thief == 'fox' and bear == 'false':
continue
if thief != hair:
continue
tally[thief] += 1
print(sorted(tally.items()))
While crude it does give the correct answer, to within 1% or so.
That everything is completely independent? This is the correct, non-naive assumption to always make unless you have a very good reason otherwise.
There are 3 binary variables. Some combinations of the variables are impossible. These impossible combinations are discarded. For example, the bear said he saw a fox. Therefor it is not possible for the bear to be truthful and the thief to be a raccoon. When that combination comes up, it is discarded. There is no dependency.
> These impossible combinations are discarded. For example, the bear said he saw a fox. Therefor [sic] it is not possible for the bear to be truthful and the thief to be a raccoon.
Per the story, there is a 20% chance a truthful bear may have mistaken a raccoon for a fox. Not automatically discarding possibilities like "a truthful bear saw a fox, though the thief is a raccoon" is a hallmark of probabilistic thinking. Thinking through these examples formally has advantages over starting with code.
But go ahead and rigorously demonstrate any non-zero existence for "A truthful bear saw a fox, though the thief is a raccoon" with the current parameters of the model. It is not a possibility, it is nonsense.
Please prove the brute-force simulation fails to converge on the correct answer. It is figuratively running a million parallel universes and recording what happened. In no legitimate universe does the combination "bear was not mistaken, bear saw fox, thief was raccoon" ever occur.
Per the discussion in the scenario, "bear was not mistaken," and "bear was truthful" are different things. One implies a bear with poor eyesight; the other implies a bear intentionally misrepresenting the facts.
Given the story, the bear mistook a raccoon for a fox 20% of the time, which is very different from being untruthful.
I'm reasonably certain no camp would claim the statistical equivalent of BogoSort as a method. 98% of the loop cycles (and 98% of the random numbers generated) make no contribution to the result and are thrown away.
There's an unsupported assumption here: we don't know that raccoons and fox have the same crime rate. Without data, I'd say that the larger animals probably have a larger rate, so it shifts more in that direction.
I'm not a teacher, and I know from friends who are that being a good teacher is harder than what I can probably imagine, but I think kids would have fun working through these types of stories.