Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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# Problem B. 4676. (December 2014)

B. 4676. A flea is jumping along the number line. It starts at the origin, and the length of each jump is 1. The probability of any jump being in the same direction as the preceding jump is $\displaystyle p$, and the probability of the opposite direction is $\displaystyle 1-p$. What is the probability that the flea will get back to the origin?

(6 pont)

Deadline expired on January 12, 2015.

### Statistics:

 42 students sent a solution. 6 points: Alexy Marcell, Csépai András, Döbröntei Dávid Bence, Gáspár Attila, Horváth Miklós Zsigmond, Katona Dániel, Kovács 246 Benedek, Nagy-György Pál, Porupsánszki István, Schwarcz Tamás, Szebellédi Márton, Williams Kada. 5 points: Baran Zsuzsanna, Bereczki Zoltán, Molnár-Sáska Zoltán, Nagy Kartal, Szakály Marcell, Zsakó Ágnes. 4 points: 4 students. 3 points: 1 student. 2 points: 2 students. 0 point: 17 students.

Problems in Mathematics of KöMaL, December 2014