Problem K. 576. (January 2018)

K. 576. A box contains some red and blue balls. If a ball is picked at random, the probability of its being blue is \(\displaystyle \frac{2}{5}\). If one blue ball is removed from the box, the probability of a randomly selected ball being red will be \(\displaystyle \frac{5}{8}\). How many balls are there in the box?

(6 pont)

Deadline expired on February 12, 2018.

Sorry, the solution is available only in Hungarian. Google translation

Megoldás. A dobozban levő golyók \(\displaystyle \frac25\) része kék. Jelölje a kékek számát \(\displaystyle 2x\), a pirosak számát \(\displaystyle 3x\). Egy kék golyót kivéve a piros húzásának valószínűsége \(\displaystyle \frac{3x}{5x-1}=\frac58\). Innen rendezéssel kapjuk, hogy \(\displaystyle 24x=25x-5\), amiből \(\displaystyle x = 5\). Tehát a dobozban \(\displaystyle 25\) golyó van (\(\displaystyle 10\) kék és \(\displaystyle 15\) piros).

Statistics:

119 students sent a solution.
6 points:	105 students.
5 points:	3 students.
2 points:	3 students.
1 point:	4 students.
0 point:	4 students.

Problems in Mathematics of KöMaL, January 2018