© 2002 Prentice-Hall, Inc.Chap 4-1 Bab 4 Probabilitas.

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1 © 2002 Prentice-Hall, Inc.Chap 4-1 Bab 4 Probabilitas

2 © 2002 Prentice-Hall, Inc. Chap 4-2 Topik Konsep dasar probabilitas Sample spaces and events, simple probability, joint probability Kondisi probabilitas Statistical independence, marginal probability Bayes’s Theorem

3 © 2002 Prentice-Hall, Inc. Chap 4-3 Topik probabilitas of a discrete random variable Binomial distribution Poisson distribution Hypergeometric distribution (continued)

4 © 2002 Prentice-Hall, Inc. Chap 4-4 Ruang Sampel Himpunan semua kemungkinan e.g.: All six faces of a die: e.g.: All 52 cards in a deck:

5 © 2002 Prentice-Hall, Inc. Chap 4-5 Kejadian Kejadian sederhana Kartu merah dari sekumpulan kartu bridge Kejadian yang saling terhubung Kartu As yang berasal dari kartu merah dan kartu hitam

6 © 2002 Prentice-Hall, Inc. Chap 4-6 Probabilitas Probabilitas menyatakan ukuran numerik dari suatu kejadian Bernilai antara 0 dan 1 Jumlah probabilitas seluruh kejadian 1 Certain Impossible.5 1 0

7 © 2002 Prentice-Hall, Inc. Chap 4-7 (There are 2 ways to get one 6 and the other 4) e.g. P ( ) = 2/36 probabilitas dari kejadian E:

8 © 2002 Prentice-Hall, Inc. Chap 4-8 Probabilitas kejadian A dan B yang saling terhubung, :

9 © 2002 Prentice-Hall, Inc. Chap 4-9 P(A 1 and B 2 )P(A 1 ) Total Event Tabel Probabilitas Kejadian yang saling terhubung P(A 2 and B 1 ) P(A 1 and B 1 ) Event Total 1 Joint Probability Marginal (Simple) Probability A1A1 A2A2 B1B1 B2B2 P(B 1 ) P(B 2 ) P(A 2 and B 2 ) P(A 2 )

10 © 2002 Prentice-Hall, Inc. Chap 4-10 Probabilitas kejadian, A or B:

11 © 2002 Prentice-Hall, Inc. Chap 4-11 P(A 1 ) P(B 2 ) P(A 1 and B 1 ) P(A 1 or B 1 ) = P(A 1 ) + P(B 1 ) - P(A 1 and B 1 ) P(A 1 and B 2 ) Total Event P(A 2 and B 1 ) Event Total 1 A1A1 A2A2 B1B1 B2B2 P(B 1 ) P(A 2 and B 2 ) P(A 2 ) For Mutually Exclusive Events: P(A or B) = P(A) + P(B)

12 © 2002 Prentice-Hall, Inc. Chap 4-12 The probabilitas kejadian B setelah kejadian A terjadi :

13 © 2002 Prentice-Hall, Inc. Chap 4-13 Black Color Type Red Total Ace 224 Non-Ace 24 48 Total 26 52 Revised Sample Space

14 © 2002 Prentice-Hall, Inc. Chap 4-14 Conditional probability: Penggandaan:

15 © 2002 Prentice-Hall, Inc. Chap 4-15 Kejadian A dan B independent jika : Kejadian A dan B independen jika probabilitas kejadian A, tidak dipengaruhi oleh kejadian lain (continued)

16 © 2002 Prentice-Hall, Inc. Chap 4-16 Bayes’s Theorem Adding up the parts of A in all the B’s Same Event