The Weekly Struggle

Probability Level 3

Every week, Brilliant reaches approximately 20,000 people via the problems of the week. We know there are 15 problems divided up into 3 categories: Beginner, Intermediate, and Advanced. After doing some rough calculations, you approximate:

On average, 75% of people correctly complete any given beginner problem
On average, 50% of people correctly complete any given intermediate problem.
On average, 25% of people correctly complete any given advanced problem.

Following these approximations, let $p$ be the expected number of people that get all 15 problems correct, assuming each problem is independent of each other. In what range does $p$ fall?

Bonus : Find the exact value of $p$ .

1≤p<20

p<1

40≤p

20≤p<40

2 solutions

Jordan Cahn
Dec 5, 2018

$\left(0.75^5\times0.50^5\times0.25^5\right)\times 20{,}000 \approx 0.14<1$

However, this assumes that the probabilities of getting each problem correct are independent, which is almost certainly not the case.

Correct. This is what the next problem will be about.

Blan Morrison - 2 years, 6 months ago

In that case, I prefer this problem. It makes me feel extra smart on weeks when I get all 15.

Jeremy Galvagni - 2 years, 6 months ago

Hahaha... Yup! :)

Geoff Pilling - 2 years, 6 months ago

I think it might be good to include that assumption in the problem itself! :)

Geoff Pilling - 2 years, 6 months ago

Why did u raise them to 5th power?

Mr. India - 2 years, 5 months ago

Because there are five questions in each category.

Jordan Cahn - 2 years, 5 months ago

A Former Brilliant Member
Dec 6, 2018

As stated in the problem description: assuming each problem is independent of each other. In what range does fall?

The Weekly Struggle

2 solutions

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