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C. 884. A roll of a die is said to be successful if the score is at least three. Which is more probable: Rolling at least once successfully out of two or at least twice out of four?

(5 points)

Deadline expired on 15 February 2007.


Google Translation (Sorry, the solution is published in Hungarian only.)

Megoldás: Annak valószínűsége, hogy egy adott dobás sikeres: 4/6=2/3.

Ennek alapján:

P(\rm{k\'et~ dob\'asb\'ol~ legal\'abb ~egy~ sikeres})=\binom{2}{1}\cdot(2/3)^1 \cdot(1/3)^1+\binom{2}{2}\cdot(2/3)^2\cdot(1/3)^0
=4/9+4/9=8/9,

P(\rm{n\'egy ~dob\'asb\'ol~ legal\'abb~ kett\H o ~sikeres})=
\binom{4}{2}\cdot(2/3)^2\cdot(1/3)^2+\binom{4}{3}\cdot(2/3)^3
\cdot(1/3)^1+\binom{4}{4}\cdot(2/3)^4\cdot(1/3)^0=

24/81+32/81+16/81=8/9.

A két esemény valószínűsége megegyezik.


Statistics on problem C. 884.
363 students sent a solution.
5 points:211 students.
4 points:26 students.
3 points:45 students.
2 points:13 students.
1 point:13 students.
0 point:55 students.


  • Problems in Mathematics of KöMaL, January 2007

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