Probabilitas kondisional

Dasar-Dasar Probabilitas di Python

Alexander A. Ramírez M.

CEO @ Synergy Vision

Kejadian saling bergantung

Kejadian saling bergantung (lanj.)

$$P(Jack) = \frac{4}{52} \simeq 7.69\%$$

Kejadian saling bergantung (lanj.)

$$P(Jack) = \frac{3}{51} \simeq 5.88\%$$

Rumus probabilitas kondisional

$$ $$

$$P(A\ dan\ B)=P(A)P(B)$$

Rumus probabilitas kondisional (lanj.)

$$ $$

$$P(A\ dan\ B)=P(A)\color{red}{P(B|A)}$$

$$ $$

$$\color{red}{P(B|A)}=\frac{P(A\ dan\ B)}{P(A)}$$

Probabilitas kondisional

Probabilitas kondisional (lanj.)

$$P(Merah|Jack)=?$$

Probabilitas kondisional (lanj.)

$$P(Merah|Jack) = \frac{P(Jack\ dan\ Merah)}{P(Jack)}$$

Probabilitas kondisional (lanj.)

$$P(Merah|Jack) = \frac{P(Jack\ dan\ Merah)}{\color{blue}{P(Jack)}}$$

Probabilitas kondisional (lanj.)

$$P(Merah|Jack) = \frac{P(Jack\ dan\ Merah)}{\color{blue}{P(Jack)}} = \frac{X}{\color{blue}{\frac{4}{52}}}$$

Probabilitas kondisional (lanj.)

$$P(Merah|Jack) = \frac{\color{red}{P(Jack\ dan\ Merah)}}{P(Jack)} = \frac{\color{red}{\frac{2}{52}}}{\frac{4}{52}}$$

Probabilitas kondisional (lanj.)

$$P(Merah|Jack) = \frac{P(Jack\ dan\ Merah)}{P(Jack)} = \frac{\frac{2}{52}}{\frac{4}{52}} = \frac{2}{4} = \frac{1}{2}$$

Probabilitas kondisional (lanj.)

$$P(Merah|Jack) = \frac{P(Jack\ dan\ Merah)}{P(Jack)} = \frac{\frac{2}{52}}{\frac{4}{52}} = \frac{2}{4} = \frac{1}{2}$$

Perhitungan P(Merah | Jack) di Python

P_Jack = 4/52
P_Jack_n_Red = 2/52

P_Red_given_Jack = P_Jack_n_Red / P_Jack

print(P_Red_given_Jack)

0.5

Probabilitas kondisional

$$P(Jack|Merah)=?$$

Probabilitas kondisional (lanj.)

$$P(Jack|Merah)=\frac{P(Merah\ dan\ Jack)}{P(Merah)}$$

Probabilitas kondisional (lanj.)

$$P(Jack|Merah) = \frac{P(Merah\ dan\ Jack)}{P(Merah)}$$

Probabilitas kondisional (lanj.)

$$P(Jack|Merah) = \frac{P(Merah\ dan\ Jack)}{\color{red}{P(Merah)}}$$

Probabilitas kondisional (lanj.)

$$P(Jack|Merah) = \frac{P(Merah\ dan\ Jack)}{\color{red}{P(Merah)}} = \frac{X}{\color{red}{\frac{26}{52}}}$$

Probabilitas kondisional (lanj.)

$$P(Jack|Merah) = \frac{\color{blue}{P(Merah\ dan\ Jack)}}{P(Merah)} = \frac{\color{blue}{\frac{2}{52}}}{\frac{26}{52}}$$

Probabilitas kondisional (lanj.)

$$P(Jack|Merah) = \frac{P(Merah\ dan\ Jack)}{P(Merah)} = \frac{\frac{2}{52}}{\frac{26}{52}} = \frac{2}{26} = \frac{1}{13}$$

Probabilitas kondisional (lanj.)

$$P(Jack|Merah) = \frac{P(Merah\ dan\ Jack)}{P(Merah)} = \frac{\frac{2}{52}}{\frac{26}{52}} = \frac{2}{26} = \frac{1}{13}$$

Perhitungan P(Jack | Merah) di Python

P_Red = 26/52
P_Red_n_Jack = 2/52

P_Jack_given_Red = P_Red_n_Jack / P_Red

print(P_of_Jack_given_Red)

0.0769230769231

Gunakan pengondisian untuk menghitung probabilitas

Dasar-Dasar Probabilitas di Python