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Week-VIII
Probability
Olasılık
(Ch-3)
Events, Sample Spaces, and Probability
(Olay, Örnek Uzay ve Olasılık)
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Tanım
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Olasılık, olayların olabilirliğinin sayılarla ifadesidir.
Günümüzde bütün bilim dallarında özellikle
ekonomi, siyaset, spor, meteoroloji ve temel
bilimlerde uygulama alanı vardır.
Günlük hayatta havaya atılan paranın ne geleceği,
bir zar atıldığında üste gelen yüzün 3 numaralı yüz
olması, şans oyunları gibi,… olayların olasılıkları
daha çok kullanılır.
Probability is starting with an animal, and figuring
out what footprints it will make.
Statistics is seeing a footprint, and guessing the
animal.
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Definition
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Deney ve Çıktı: Bir madeni paranın havaya
atılması sonucuna iki durum vardır. Üste
gelen yüz tura veya yazıdır. Burada paranın
atılması olayına deney, gelebilecek
sonuçlara da çıktı denir.
Definition
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Bir deneyde elde edilebilecek tüm çıktıların
kümesine örnek uzay denir ve S ile
gösterilir. Örnek uzayın çıktılarının her birine
örnek nokta denir.
Figure 3.1 Tree diagram for the coin-tossing
experiment
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Figure 3.2 Venn diagrams for the three
experiments from Table 3.1
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Figure 3.3 Proportion of heads in N tosses
of a coin
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Figure 3.4 Experiment: invest in a business
venture and observe whether it succeeds (S)
or fails (F)
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Procedure
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Figure 3.5 Die-toss experiment with event
A, observe an even number
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Definition
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Bir deneyin örnek uzayının alt kümelerinden
her birine olay, S örnek uzayına kesin olay,
boş kümeye imkansız olay denir.
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Definition
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Procedure
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Table 3.2
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Table 3.3
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Procedure
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Exercises
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3.2
Unions and Intersections
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Definition
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Definition
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Figure 3.7 Venn diagrams for union and
intersection
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Figure 3.8 Venn diagrams for die toss
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3.3
Complementary Events
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Definition
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Figure 3.9 Venn diagrams of
complementary events
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Procedure
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Figure 3.10 Complementary events in the
toss of two coins
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3.4
The Additive Rule and
Mutually Exclusive (Ayrık) Events
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Figure 3.11 Venn diagram of union
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Procedure
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Figure 3.12 Venn diagram of Mutually
exclusive events
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Definition
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Procedure
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Figure 3.13 Venn diagram for coin-toss
experiment
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Exercises
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3.5
Conditional Probability
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Figure 3.14 Reduced sample space for the
die-toss experiment: given that event B has
occurred
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Formula
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Figure 3.15 Sample space for Example 3.15
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Table 3.5
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Table 3.6
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3.6
The Multiplicative Rule and
Independent Events
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Procedure
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Figure 3.16 Venn diagram for finding P(A)
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Figure 3.17 Venn diagram for finding P(B|A)
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Figure 3.18 Tree diagram for Example 3.17
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Definition
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Figure 3.19 Venn diagram for die-toss
experiment
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Figure 3.20 Mutually exclusive events are
dependent events
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Procedure
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Exercises
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3.7
Random Sampling
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Definition
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Table 3.7
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Figure 3.21 MINITAB worksheet with
random sample of 50 households
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Figure 3.22 MINITAB worksheet with
random assignment of physicians
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Exercises
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3.8
Some Additional Counting Rules (Optional)
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Figure 3.23 Tree diagram for shipping
problem
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Procedure
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Procedure
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Table 3.8
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Table 3.9
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Procedure
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Definition
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Exercises
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3.9
Bayes’s Rule (Optional)
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Figure 3.24 Tree diagram for Example 3.33
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Procedure
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Exercises
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