AIME 2015 Problem 2

Probability Level 3

In a new school 40 percent of the students are freshmen, 30 percent are sophomores, 20 percent are juniors, and 10 percent are seniors. All freshmen are required to take Latin, and 80 percent of the sophomores, 50 percent of the juniors, and 20 percent of the seniors elect to take Latin. The probability that a randomly chosen Latin student is a sophomore is $\dfrac{m}{n}$ , where $m$ and $n$ are relatively prime positive integers. Find $m+n$ .

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The answer is 25.000.

2 solutions

Alex Wang
Jan 30, 2020

100 people in school, then there are 40 freshmen, 24 sophomores, 10 juniors, 2 seniors take latin. 24/76=6/19. 6+19=25.

Brandon Monsen
Dec 3, 2015

we can deduce from the conditions given in the problem in a school of sample size 100 that $40$ freshmen take Latin, $24$ sophomores take Latin, $10$ juniors take Latin and $2$ seniors take Latin.

The probability that a sophomore is chosen is $\frac{24}{40+24+10+2}$ , which reduces to $\frac{6}{19}$ , so our answer is $6+19=\boxed{25}$

Again did the same way and again the problem is overrated :).

A Former Brilliant Member - 5 years, 6 months ago

AIME 2015 Problem 2

Try more problems of AIME from this set AIME 2015

The answer is 25.000.

2 solutions

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