Mathematical and Physical Journal
for High Schools
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Problem C. 884. (January 2007)

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 pont)

Deadline expired on February 15, 2007.


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

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:

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