The Weekly Confusion
Probability
Level
2
In the last problem , it was approximated that, out of 20,000 people, only a small portion solve all 15 problems of the week. However, is this approximation is flawed. Why?
Skill level among users needs to be factored in.
All of these answers can be correct.
The theoretical approximation does not even come close to reality.
The probabilities of getting each problem correct are not necessarily independent.
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1 solution
All of the choices given are valid explanations.
Less skilled users might attempt the advanced problems and may try guessing, which will bring down the advanced and intermediate averages. If this wasn't the case and it was 75% for all problems, then we would expect 2 0 0 0 0 ∗ . 7 5 1 5 ≈ 2 6 7 people to get all the problems right. However, those people would all be advanced level, which isn't necessarily the case in reality.
If we followed the approximation from the last problem, which is about .14 people, that would mean this would happen once every 7 weeks, or about 7 times a year. However, this is most certainly not the case.
As @Jordan Cahn pointed out, the probabilities of getting each problem correct are more than likely somewhat dependent. For instance, if you incorrectly answer the first three beginner problems in a row, you might get demoralized and perform worse on the other two problems. The human mind is a brilliant, complicated, and strange machine.
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