1. PROBABILITY

2. PROBABILITY Medicine is an inexact science
Physicians can rarely predict an outcome with absolute certainty.
Results of available diagnostic tests are not necessarily absolutely accurate, but it definitely affect the probability of presence or absence of disease

3. PROBABILITY
The theory of probability underlies the methods for drawing statistical inferences in medicine through quantifying the uncertainty inherent in the decision –making process

4. PROBABILITY
Probability theory allows clinicians to draw conclusions about a population of patients based on known information about a sample drawn from that population.

5. PROBABILITY
It is the likelihood of occurrence of a certain event compared to the total events

6. PROBABILITY no. of times E occurs
P(E)=
no. of times E can occur
P(E): Probability of occurrence of event E
The probability of an event is a non-negative number
0 ≤ P (E) ≤ 1

7. PROBABILITY Probability values lie between 0 and 1
A value of 0 means the event can not occur
A value of 1 means the event will definitely occur
A value of 0.5 means that the probability of occurrence of the event is equal to the probability of non-occurrence of that event

8. PROBABILITY
The sum of the probabilities (or relative frequencies) of all event that can occur in the sample must be 1 (or 100%)

9. Distribution of S.Cholesterol values (mg/dl) of 1047 individuals
CRF%
RF%
frequency
S.Cholesterol
(mg/dl) 3 31
<160
15.8
12.8
134
50.0
34.2
358
81.1
31.1
326
94.8
13.7
145
98.9
4.1 43
100
1.2 12
360+
1047
total

10. 2 x 2 table (F + ve ) (T + ve ) (T -ve ) (F - ve ) 11 4 7 89 86 3
Total
Disease
-ve
Disease ve 11 4
(F + ve ) 7
(T + ve )
Test +ve 89 86
(T -ve ) 3
(F - ve )
Test -ve
100 90 10

11. 2 x 2 table T+ means the persons have the disease & they show test +ve
F+ (false +ve) means the persons have no disease & they show test +ve
F- (false –ve) means the persons have the disease & they show test –ve

12. Marginal Probabilities
P(D+) =
= 10/100=0.1 = 10%
P(D-) =
=90/100= 0.9 =90%
P(T+) =
=11/100 = 0.11=11%
P(T-) =
=89/100 = 0.89 =89%
Total
Disease
-ve
Disease ve 11 4 7
Test +ve 89 86 3
Test
100 90 10

13. Joint probability
The probability of occurrence of two or more events simultaneously
P(A and B)

14. Joint probability P(D+&T+) = =7/100=0.07 =7% P(D-&T+) =
=7/100=0.07 =7%
P(D-&T+) =
=4/100= 0.04 =4%
P(T-&D+) =
=3/100 = 0.03=3%
P(T-&D-) =
=86/100 = 0.86=86%
Total
Disease
-ve
Disease ve 11 4 7
Test +ve 89 86 3
Test
100 90 10

15. Conditional probability
The probability of occurrence of an event given that another event had already occurred
P (B I A) = P (B and A) / P(A)
Occurrence of event B when event A had already occurred

16. Conditional probability
P(D+ I T+)
= P(D+&T+) / P(T+)
=(7/100) / (11/100)
=7/11
=63.64%
Total
Disease
-ve
Disease ve 11 4 7
Test +ve 89 86 3
Test
100 90 10

17. Conditional probability
P(D- I T+)
=P(D-&T+) / P(T+)
= (4/100) / (11/100)
=4/11
=36.36%
Total
Disease
-ve
Disease ve 11 4 7
Test +ve 89 86 3
Test
100 90 10

18. Multiplication rules Independent events:
If the occurrence of event A is not affected by occurrence of event B
P(A and B) = P(A) X P(B)
Multiplication rules of probability
(when “ and” is used)

19. Multiplication rules / Independent events
CRF%
R F%
No.
S.Ch
(mg/dl) 3 31
<160
15.8
12.8
134
50.0
34.2
358
81.1
31.1
326
94.8
13.7
145
98.9
4.1 43
100
1.2 12
360+
1047
total
What is the probability of selecting two patients randomly , both of them had S. cholesterol level of <160 mg/dl?
=0.03 X 0.03 =
=0.09%

20. Multiplication rules/ Independent events
What is the probability of having two boys in two successive pregnancies?
= 0.5 X 0.5 = 0.25
=25%

21. Multiplication rules Non independent events
Occurrence of event A is affected by occurrence of event B (if the two events are related or associated)
P (A and B) = P (A I B) . P (B)
So it is joint probability

22. Multiplication rules/ Non independent events
What is the probability
of selecting an
individual who is
disease –ve & test –ve?
P(D- and T -)
=86/100
= 86%
Total
Disease
-ve
Disease ve 11 4 7
Test +ve 89 86 3
Test -ve
100 90 10

23. Probability rules
Addition rules of probabilities
When “or” is used

24. Addition rules Mutually exclusive events:
the events that can not occur together,
i.e.: the occurrence of one event will exclude the occurrence of the other event
P(A or B)= P(A) + P(B)

25. Addition rules/ Mutually exclusive events
What is the probability of selecting at random a person with serum cholesterol of <160 or > 360 mg/dl
P(S.ch<160)+P(S.ch>360)
= 3%+1.2% = 4.2%
CRF%
R F%
No.
S.Ch
(mg/dl) 3 31
<160
15.8
12.8
134
50.0
34.2
358
81.1
31.1
326
94.8
13.7
145
98.9
4.1 43
100
1.2 12
360+
1047
total

26. Addition rules Non mutually exclusive events P(A or B)
= P(A)+ P(B) – P(A and B)

27. Addition rules/ Non mutually exclusive events
P(D- or T-)
= P(D-) + P(T-) – P(D- and T-)
= (90/100)+ (89/100)-(86/100)
=93/100
=93%
Total
Disease
-ve
Disease ve 11 4 7
Test +ve 89 86 3
Test -ve
100 90 10

28. Exercise Results of blood type and sex of 100 individuals.
What is the probability that an individual picked at random from this group has:
P( Female I B.group A)
P(B.group A I Female)
Total
Female
Male 40 20 O 35 18 17 A 15 7 8 B 10 5 AB
100 50

29. Exercise P(B.group O or A) P(B.Group O and Male) P(B.group AB I Male)
P( Male &B.group B)
P(Female & B.group O)
P( Male or B.group AB)
P(B.group B)
Total
Female
Male 40 20 O 35 18 17 A 15 7 8 B 10 5 AB
100 50

30. Exercise Total Not ill ill 120 30 90 Ate Fish 80 60 20
Did not eat Fish
200
110

31. Exercise
What is the probability that a student becomes ill after eating Fish?
What is the probability that a student does not become ill after eating Fish?
What is the probability that a student becomes ill if no Fish is eaten?

32. Exercise
What is the probability that a student who attended the party becomes ill?
What is the probability that a student with food poisoning ate Fish?
What is the probability that a student who attended the party did not eat Fish?

33. Exercise
The following table shows the outcome of 500 interviews completed during a survey to study the opinions of residents of a certain city about legalized abortion. The data are also classified by the area of the city in which the questionnaire was attempted.
Outcome
Area of city
For(F)
Against(Q)
Undecided(R) A
100 20 5
125 B
115 C 50 60 15 D 35 40
300
135 65
500
Calculate the following probabilities:
1- P(A and R) P( Q or D)
3- P( D) P( Q/D) P( B/R)