Probability (Olasılık)

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Presentation transcript:

Probability (Olasılık) Chapter 3 Probability (Olasılık)

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

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

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

Figure 3.1 Tree diagram for the coin-tossing experiment Copyright © 2013 Pearson Education, Inc.. All rights reserved.

Figure 3.2 Venn diagrams for the three experiments from Table 3.1 Copyright © 2013 Pearson Education, Inc.. All rights reserved.

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

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

Figure 3.3 Proportion of heads in N tosses of a coin Copyright © 2013 Pearson Education, Inc.. All rights reserved.

Figure 3.4 Experiment: invest in a business venture and observe whether it succeeds (S) or fails (F) Copyright © 2013 Pearson Education, Inc.. All rights reserved.

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

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

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

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

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

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

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

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

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

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

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

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

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

Figure 3.7 Venn diagrams for union and intersection Copyright © 2013 Pearson Education, Inc.. All rights reserved.

Complementary Events Tamamlayıcı Olaylar 3.3 Complementary Events Tamamlayıcı Olaylar

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

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

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

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.

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

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

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

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

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

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

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.

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

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

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

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

Conditional Probability Koşullu Olasılık 3.5 Conditional Probability Koşullu Olasılık

Figure 3.14 Reduced sample space for the die-toss experiment: given that event B has occurred Copyright © 2013 Pearson Education, Inc.. All rights reserved.

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.

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

Table 3.5 Copyright © 2013 Pearson Education, Inc.. All rights reserved.

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

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

Figure 3.16 Venn diagram for finding P(A) Copyright © 2013 Pearson Education, Inc.. All rights reserved.

Figure 3.17 Venn diagram for finding P(B|A) Copyright © 2013 Pearson Education, Inc.. All rights reserved.

Figure 3.18 Tree diagram for Example 3.17 Copyright © 2013 Pearson Education, Inc.. All rights reserved.

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

Figure 3.19 Venn diagram for die-toss experiment Copyright © 2013 Pearson Education, Inc.. All rights reserved.

Figure 3.20 Mutually exclusive events are dependent events Karşılıklı kapsamayan olaylar bağımsız olaylardır. Copyright © 2013 Pearson Education, Inc.. All rights reserved.

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

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

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

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

Random Sampling Rastgele Örnekleme 3.7 Random Sampling Rastgele Örnekleme

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

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

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

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

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

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