Perumusan Probabilitas: Klasik dan Relatif
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Perumusan Probabilitas: Klasik dan Relatif

Jumat, 17 Juli 2020

Konsep probabilitas atau teori peluang dapat dirumuskan dengan dua cara, yaitu: klasik dan frekuensi relatif. Perlu dingat lagi bahwa probabilitas dilambangkan dengan huruf " P " kapital, sehingga jika ada suatu kejadian (K) maka dapat dirumuskan dengan P(K).

 

Sebelum melanjutkan bacaan, ada baiknya ada bekal pengetahuan tentang teori probabilitasyang dapat dibaca pada artikel Teori Peluang: Pengertian Probabilitas.

 

Perumusan Klasik
Apabila kejadian K terjadi dalam x cara dari seluruh n cara yang mungkin terjadi dan setiap n cara memiliki kemungkinan sama untuk muncul, maka probabilits kejadian K dirumuskan sebagai berikut:

 

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Contoh

Sebuah koin 1.000 rupiah dengan dua sisi yang masing-masing berupa angklung dan angka 1000 punya kesempatan sama untuk muncul. Apabila sisi angklung disebut SA dan sisi angka disebut SB maka probabilitas munculnya kejadian (K), yaitu:

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atau bisa juga ditulis bahwa probabilitas kejadian K, yaitu:

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Hasil di atas menunjukkan bahwa semua kejadian munculnya sisi A dan sisi B mempunyai besar yang sama yaitu 0,5. Hal tersebut seringkali disebut sebagai kelemahan dari perumusan klasik, karena mensyaratkan semua hasil harus memiliki peluang sama untuk muncul. Kelemahan tersebut menjadikan penggunaan perumusan klasik kurang diterima dimasa kini, untuk kemudian digantikan dengan perumusan menggunakan frekuensi relatif.


Perumusan Frekuensi Relatif
Probabilitas yang dikembangkan dengan pendekatan empiris menggunakan frekuensi relatif suatu kejadian yang mensyaratkan banyaknya sampel dalam jumlah besar. Oleh karena sampel yang digunakan dalam jumlah besar, sangat besar, atau bahkan tak terhingga maka probabilitas dari kejadian K menjadi sama dengan batas nilai frekuesi relatif dari kejadian K.

 

Dapat pula dikatakan jika kejadian K yang terjadi sebanyak k kali dari seluruh pengamatan n dengan n mendekati tak terbatas maka probabilitas kejadian K dirumuskan sebagai berikut:

 

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Namun, perumusan dengan frekuensi relatif mempunyai kelemahan yang menunjukkan bahwa batas nilai sesungguhnya bisa jadi tidak ada. Sehingga, konsep probabilitas terbaru yang digunakan menggunakan pendekatan aksiomatris yang menerima kebenaran apa adanya tanpa perlu bukti matematis.

 

Contoh

Sebuah dadu berwarna putih dengan angka berbeda setiap sisinya: 1,2,3,4,5,6 yang ditandai dengan titik-titik hitam menunjukkan bahwa semua angka dadu punya kesempatan/peluang sama untuk muncul. Dadu dilempar sebanyak seratus kali (n=100) maka frekuensi munculnya angka x dapat dilihat pada tabel di bawah ini.

 

Angka Dadu (X) 1 2 3 4 5 6
Frekuensi (F) 12 13 26 29 14 6

 

Kejadian munculnya angka dadu dilambangkan K, maka diperoleh K= {1}, {2},{3}, {4}, {5}, {6} atau dibaca kejadian munculnya angka 1,2,3,4,5,6. Sehingga probabilitas kejadian K untuk kemungkinan munculnya angka dadu, yaitu:

 

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Jadi, probabilitas atau kemungkinan munculnya angka dadu 1 adalah 0,12 dan seterusnya pula untuk angka dadu 2,3,4,5, dan 6.

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