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Probability (Olasılık)

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Presentation on theme: "Probability (Olasılık)"— Presentation transcript:

1 Probability (Olasılık)
Chapter 3 Probability (Olasılık)

2 Events, Sample Spaces, and Probability
3.1 Events, Sample Spaces, and Probability

3 Definition Copyright © 2013 Pearson Education, Inc.. All rights reserved.

4 Definition Copyright © 2013 Pearson Education, Inc.. All rights reserved.

5 Figure 3.1 Tree diagram for the coin-tossing experiment
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6 Figure 3.2 Venn diagrams for the three experiments from Table 3.1
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7 Definition Copyright © 2013 Pearson Education, Inc.. All rights reserved.

8 Table 3.1 Copyright © 2013 Pearson Education, Inc.. All rights reserved.

9 Figure 3.3 Proportion of heads in N tosses of a coin
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10 Figure 3.4 Experiment: invest in a business venture and observe whether it succeeds (S) or fails (F)
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11 Procedure Copyright © 2013 Pearson Education, Inc.. All rights reserved.

12 Figure 3.5 Die-toss experiment with event A, observe an even number
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13 Definition Copyright © 2013 Pearson Education, Inc.. All rights reserved.

14 Definition Copyright © 2013 Pearson Education, Inc.. All rights reserved.

15 Procedure bir nesne grubu (N) içerisinden, sıra gözetmeksizin yapılan seçimler (n) Copyright © 2013 Pearson Education, Inc.. All rights reserved.

16 Copyright © 2013 Pearson Education, Inc.. All rights reserved.

17 Copyright © 2013 Pearson Education, Inc.. All rights reserved.

18 Copyright © 2013 Pearson Education, Inc.. All rights reserved.

19 Hw. 3 20 15504 Copyright © 2013 Pearson Education, Inc.. All rights reserved.

20 Copyright © 2013 Pearson Education, Inc.. All rights reserved.

21 Unions and Intersections Birleşim ve Kesişim
3.2 Unions and Intersections Birleşim ve Kesişim

22 Definition Copyright © 2013 Pearson Education, Inc.. All rights reserved.

23 Definition Copyright © 2013 Pearson Education, Inc.. All rights reserved.

24 Figure 3.7 Venn diagrams for union and intersection
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25 Complementary Events Tamamlayıcı Olaylar
3.3 Complementary Events Tamamlayıcı Olaylar

26 Definition Copyright © 2013 Pearson Education, Inc.. All rights reserved.

27 Figure 3.9 Venn diagrams of complementary events
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28 Procedure Copyright © 2013 Pearson Education, Inc.. All rights reserved.

29 Figure 3.10 Complementary events in the toss of two coins
A= {Havaya atılan iki paradan en az birinin yazı gelmesi} Copyright © 2013 Pearson Education, Inc.. All rights reserved.

30 3.4 The Additive Rule and Mutually Exclusive Events Ekleme Kuralı ve
Karşılıklı Kapsamayan (Bağımsız) Olaylar

31 Figure 3.11 Venn diagram of union
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32 Procedure Copyright © 2013 Pearson Education, Inc.. All rights reserved.

33 Figure 3.12 Venn diagram of Mutually exclusive events
Karşılıklı kapsamayan olaylar için venn şeması Copyright © 2013 Pearson Education, Inc.. All rights reserved.

34 Ortak elemanları olmayan A ve B kümeleri
Definition Ortak elemanları olmayan A ve B kümeleri Copyright © 2013 Pearson Education, Inc.. All rights reserved.

35 Procedure Copyright © 2013 Pearson Education, Inc.. All rights reserved.

36 Figure 3.13 Venn diagram for coin-toss experiment
A= {Havaya atılan iki paradan en az birinin yazı gelmesi} B= {Havaya atılan iki paradan en fazla birinin yazı veya tura gelmesi} C= {Havaya atılan iki paranın yazı gelmesi} Copyright © 2013 Pearson Education, Inc.. All rights reserved.

37 Copyright © 2013 Pearson Education, Inc.. All rights reserved.

38 Copyright © 2013 Pearson Education, Inc.. All rights reserved.

39 Hw. Copyright © 2013 Pearson Education, Inc.. All rights reserved.

40 Copyright © 2013 Pearson Education, Inc.. All rights reserved.

41 Conditional Probability Koşullu Olasılık
3.5 Conditional Probability Koşullu Olasılık

42 Figure 3.14 Reduced sample space for the die-toss experiment: given that event B has occurred
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43 B olayı belli iken A olayının koşullu (gerçekleşme) olasılığı
Formula B olayı belli iken A olayının koşullu (gerçekleşme) olasılığı Copyright © 2013 Pearson Education, Inc.. All rights reserved.

44 Figure 3.15 Sample space for Example 3.15
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45 Table 3.5 Copyright © 2013 Pearson Education, Inc.. All rights reserved.

46 The Multiplicative Rule and Independent Events
3.6 The Multiplicative Rule and Independent Events Çarpım Kuralı ve Bağımsız Olaylar

47 Procedure Copyright © 2013 Pearson Education, Inc.. All rights reserved.

48 Figure 3.16 Venn diagram for finding P(A)
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49 Figure 3.17 Venn diagram for finding P(B|A)
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50 Figure 3.18 Tree diagram for Example 3.17
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51 Definition Copyright © 2013 Pearson Education, Inc.. All rights reserved.

52 Figure 3.19 Venn diagram for die-toss experiment
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53 Figure Mutually exclusive events are dependent events Karşılıklı kapsamayan olaylar bağımsız olaylardır. Copyright © 2013 Pearson Education, Inc.. All rights reserved.

54 Procedure Copyright © 2013 Pearson Education, Inc.. All rights reserved.

55 Copyright © 2013 Pearson Education, Inc.. All rights reserved.

56 Copyright © 2013 Pearson Education, Inc.. All rights reserved.

57 Copyright © 2013 Pearson Education, Inc.. All rights reserved.

58 Random Sampling Rastgele Örnekleme
3.7 Random Sampling Rastgele Örnekleme

59 Definition Copyright © 2013 Pearson Education, Inc.. All rights reserved.

60 Table 3.7 Copyright © 2013 Pearson Education, Inc.. All rights reserved.

61 Copyright © 2013 Pearson Education, Inc.. All rights reserved.

62 Copyright © 2013 Pearson Education, Inc.. All rights reserved.

63 Copyright © 2013 Pearson Education, Inc.. All rights reserved.

64 Copyright © 2013 Pearson Education, Inc.. All rights reserved.


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