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A. Juriˇ<strong>si</strong>ć in V. Batagelj: Verjetnostni račun in statistika 267 ✬ ✫ V poljubni skupini 23-ih ljudi je verjetnost, da imata vsaj dva skupni rojstni dan > 1/2. Čeprav je 23 majhno ˇstevilo, je med 23 osebami 253 različnih parov. To ˇstevilo je veliko bolj povezano z iskano verjetnostjo. Testirajte to na zabavah z več kot 23 osebami. Organizirajte stave in dolgoročno boste gotovo na boljˇsem, na velikih zabavah pa boste zlahka zmagovali. Univerza v Ljubljani ▲ ❙ ▲ ▲ ● ❙ ▲ ▲ ☛ ✖ ▲ ✩ ✪
A. Juriˇ<strong>si</strong>ć in V. Batagelj: Verjetnostni račun in statistika 268 ✬ ✫ Napad s pomočjo paradoksa rojstnih dnevov (angl. Birthday Attack) To seveda ni paradoks, a vseeno ponavadi zavede naˇs občutek. Ocenimo ˇse sploˇsno verjetnost. Mečemo k ˇzogic v n posod in gledamo, ali sta v kakˇsni posodi vsaj dve ˇzogici. Poiˇsčimo spodnjo mejo za verjetnost zgoraj opisanega dogodka: 1 − 1 1 − n 2 · · · 1 − n k − 1 n k−1 = 1 − i n Univerza v Ljubljani ▲ ❙ ▲ ▲ i=1 ● ❙ ▲ ▲ ☛ ✖ ▲ ✩ ✪
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✬ ✫ Ljubljana, 6. oktober 2008
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A. Juriˇsić in V. Batagelj: Verje
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