Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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Problem C. 1109. (January 2012)

C. 1109. There were 14 multiple choice questions on a quiz, with 4 answers to each question. The best score was 10. What is the probability of achieving this score if the answers are selected at random?

(5 pont)

Deadline expired on February 10, 2012.

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


\(\displaystyle \binom{14}{10}\cdot \left ( \frac 14\right)^{10} \cdot \left ( \frac 34\right)^{4}\approx 0,0003.\)


280 students sent a solution.
5 points:184 students.
4 points:8 students.
3 points:11 students.
2 points:40 students.
1 point:16 students.
0 point:9 students.
Unfair, not evaluated:12 solutionss.

Problems in Mathematics of KöMaL, January 2012