Sise sumber ni Probabilitas

'''Probabilitas''' sanga '''Peluang''' '''Abisajadian''' ima cara giot mangungkapkon parbinotoan sanga kapurcayaan molo sada kajadian nangkan malaku sanga madung tarjadi. Konsep on madung irumuskon dohot lobi kotat i [[matematika]], dot sidungi ipake bahat i inda umna i matematika sanga [[statistika]], tai juo [[keuangan]], [[sains]] dot [[filsafat]].

== Konsep matematika ==
{{Main| teori probabilitas}}
Probabilitas sada [[kajadian (teori probabilitas)|kajadian]] ima angko na patidaon kamungkinan tarjadina sada kajadian. Nilena i antara 0 dot 1. Kajadian na puna nile probabilitas 1 ima kajadian na pasti tarjadi sanga sangaaha na madung tarjadi<ref name="Sheldon Ross">{{en}}. A First Course in Probability - Sheldon Ross 1976</ref>. Misalna [[mataniari]] na lek terbit i [[timur]] sampe saonnari. Sadangkan sada kajadian na puna nile probabilitas 0 ima kajadian naso mungkin sanga mustahil tarjadi. Misalna sapasang ambeng mangalahirkon sada lombu.

Probabilitas/Peluang sada kajadian ''A'' tarjadi ilambangkon dohot notasi P(''A''), p(''A''), sanga Pr(''A''). Sabalikna, probabilitas [inda A] sanga ''komplemen A'', sanga probabilitas sada kajadian ''A'' inda nangkan tarjadi, ima 1-P(''A''). Contona, peluang anso inda rona mata dadu onom molo sada dadu marsisi onom igulangkon ima <math>1-\frac{1}{6} = \frac{5}{6}</math>

== Kajadian saling bebas ==
Dua kajadian <math> A </math> dot <math> B </math> idokon '''saling bebas''' molo
:<math>\mathrm{P}(A \cap B) = \mathrm{P}(A)\mathrm{P}(B)</math>.

Sanga

:<math>\mathrm{P}(A \cap B) = \mathrm{P}(A)\mathrm{P}(B) \Leftrightarrow \mathrm{P}(A) = \frac{\mathrm{P}(A) \mathrm{P}(B)}{\mathrm{P}(B)} = \frac{\mathrm{P}(A \cap B)}{\mathrm{P}(B)} = \mathrm{P}(A\mid B)</math>.

sarupona

:<math>\mathrm{P}(A \cap B) = \mathrm{P}(A)\mathrm{P}(B) \Leftrightarrow \mathrm{P}(B) = \mathrm{P}(B\mid A)</math>.

== Frekuensi aropan ==
Rumus frekuensi aropan ima:
:<math>\mathrm{F}(A) = \mathrm{n}(A)\mathrm{P}(A)</math>.

;Conto:
:# I sada kotak adong 5 bal narara, 4 bal nabalau dot 3 bal nalomlom. Tolu bal ibuat sakaligus tingon bagasan kotak sacara acak. Pigama peluang molo bal na tarbuat ima 2 bal narara dot 1 bal nalomlom?

:<math>P = {\frac{C^5_2 \, C^3_1}{C^{12}_3}} =  {\frac{{\frac{5!}{2! \, 3!}} \, {\frac{3!}{1! \, 2!}}}{{\frac{12!}{3! \, 9!}}}} = {\frac{3}{22}} </math>

:# I sada karanjang adong 7 bal narara, 5 bal nabalau dot 8 bal nalomlom. Molo ibuat 3 bal sacara acak '''dohot sarat''' bal na ibuat ipaulak mulak tu bagasan karanjang, pigama peluang molo bal na tarbuat sacara marturut-turut marwarna narara,nalomlom dot nabalau?

:<math>P = {\frac{7}{20}} \,  {\frac{8}{20}} \,  {\frac{5}{20}} =  {\frac{7}{200}} </math>

:# I sada kotak adong 5 bal narara, 6 bal narata dot 4 bal nagorsing. Molo ibuat 3 bal sacara acak '''indadong''' naipaulak, pigama peluang bal na tarbuat sacara marturut-turut ima narara, narata, nagorsing?

:<math>P = {\frac{5}{15}} \,  {\frac{6}{14}} \,  {\frac{4}{13}} =  {\frac{4}{91}} </math>

:# Dua buah dadu irambankon sumbarang rap sakali. Pigama peluang ro bahat padua mata dadu 4 sanga 7?
:<math>\mathrm{P}(4) = \frac{3}{6^2} \, = \frac{3}{36} \, </math>
:<math>\mathrm{P}(7) = \frac{6}{6^2} \, = \frac{6}{36} \, </math>
:<math>\mathrm{P}(4 \cup 7) = \mathrm{P}(4) + \mathrm{P}(7) = {\frac{3}{36}} \, + {\frac{6}{36}} \, = {\frac{1}{4}} </math>

:# Ading sarombongon ima tingon 3 daganak. Pigama peluang ro lobi tingon sada daganak alaklai?
:<math>\mathrm{P}(2L \cap 1P) = \frac{3}{2^3} = {\frac{3}{8}} </math>
:<math>\mathrm{P}(3L) = \frac{1}{2^3} = {\frac{1}{8}} </math>
:<math>\mathrm{P}(> 1 L) = \mathrm{P}(2L \cap 1P) + \mathrm{P}(3L) = \frac{3}{8} \, + \frac{1}{8} \, = \frac{1}{2} </math>

== Ligin muse ==
* [[Teori peluang]]

== Sumberna ==
{{Reflist}}

{{bidang matematika}}

[[Kategori:Peluang| ]]