1. University of Medicine 1, Yangon
Basic Statistics Course (2023)
Basic Concept of Probability
D R . N YA N L I N N
L E C T U R E R
D E PA RT ME N T O F P R E V E N T I VE A N D S O C I A L ME D I C I N E
4. Probability is usually expressed by the notion/symbol P(A)
It range from zero to one.
If an outcome is sure to occur, it has a probability of one
If an outcome cannot occur, its probability is zero.
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5. Probabilities vary between “0” and “1”
0 P (E) 1
Expressing probability
P(E) = 0.05
we expect that event to occur 5% of the time
the chances that event will occur are 5 in 100
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6. Mutually exclusive event
the occurrence of two events cannot occur
simultaneously the occurrence of any one
event means that none of the others can occur
at the same time
Independent event
The occurrence of one event has no effect on
the possibility of the occurrence of any other
event
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7. Views of Probability
1. Subjective probability
is personalistics
based on the beliefs of the person making the probability assessment
which reflects a person’s opinion, experience, common sense
not accepted by statisticians
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8. Prior probability
based on prior knowledge, prior
experience, or results derived from prior
data collection activity.
Posterior probability
obtained by using new information to
update or revise a prior probability.
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10. 2. Objective probability
(1) Classical probability (Priori Probability)
When six sided dice is rolled,
no. of favorable outcome
P (occurrence of E) =
no. of all possible outcomes
P(2) = 1 / 6
When playing 52 cards and if one is to be drawn,
P(picking a heart) = 13 / 52
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11. Classical probability (three assumptions)
(a) Mutually exclusive
The occurrence of two events do not occur
simultaneously
The occurrence of any one event means that none
of the others can occur at the same time.
(b)Collectively exhaustive (types of profession
chosen by students completed from a high school)
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12. Classical probability (Continued:)
(c)Equally likely –i.e equally probable
When a card is taken at random from a well-shuffled deck,
all possible outcomes are "equally likely”
Eg, we all know that the probability of tipping a fair coin &
getting a “tail” is 0.5 or 50%
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Head
50%
Tail
50%
Fair coin
13. (2) Relative frequency probability
When the process is repeated, a large number of times “n”
and the event “m” times have occurred, then
m
P(E) =
n
Example of relative frequency probability
1. Probability of ever been to foreign countries among
students
2. Probability of new live-born in a population
3. Probability of die during first year of life
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14. Properties of probability
1. The probability of any event must not be negative
numbers
P(E) ≥ 0
2. The sum of the probability of all mutually exclusive
outcomes is equal to
P(E1) + P(E2) + …….+ P(En) = 1
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15. 3. (a) In mutually exclusive events,
P(E1 or E2) = P(E1) + P(E2)
3. (b) In not mutually exclusive events,
P(E1 or E2) = P(E1) + P(E2) - P(E1 and E2)
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Teacher Doctor
also
16. Rules of Probability
(1) Additive rule
(a) If E1 & E2 are mutually exclusive events
eg. A thrown dice will show a one or a two but not both
(or) Prob: that it will show a one or a two is
P (one or two) = 1/6 + 1/6 = 2/6
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P (E1 or E2) = P (E1) + P(E2)
P (E1 ∪ E2) = P (E1) + P(E2)
17. (b)If E1 and E2 are not mutually exclusive events, there is
overlapping of the categories
Eg. A study among 1000 patients 200 abused alcohol. 100 abused
drug and 20 abused both. Probability that a given patient is either
alcohol or drug abuser is
P(A or D) = 200/1000 + 100/1000 – 20/1000
= 280/1000
= 0.28
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P (E1 or E2) = P (E1) + P(E2) – P (E1 and E2)
P (E1 ∪ E2) = P (E1) + P(E2) – P (E1 ∩ E2)
18. (2) Multiplicative rule
If two events are Independent,
Eg. On physical examination of a child, dental caries
and scabies are found.
If two events are not independent,
Eg. She cannot go to school as she is sick.
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P (A and B) = P (A) x P(B)
P (A and B) = P (A) x P(BA) (or) P (B) x P (AB)
P (A∩B) = P (A) x P(B)
P (A ∩ B) = P (A) x P(BA) (or) P (B) x P (AB)
19. (3) Complementary rule
Two events are complementary if they are opposite
P(A) + P(Ā) = 1
P(A) = 1-P(Ā)
P(Ā) = 1-P(A)
Complementary events are mutually exclusive
Eg. male / female survival / death
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Ā A
P(A) = 1- P(not A) or
P(not A) = 1- P(A)
20. Types of probability
(1) Marginal probability : the probability of one of the marginal
total is used as numerator and the total group as the
denominator.
Eye Glass
wearing
Eye Glass not
wearing
Total
Male 10 40 50
Female 5 45 50
Total 15 85 100
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20
21. Marginal Total
P (Male) =
Grand total
P (Male) = 50 / 100
Marginal Total
P(eye glass wearing) =
Grand total
P(E+) = 15 / 100
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Eye
Glass
wearing
Eye Glass
not wearing
Total
Male 10 40 50
Female 5 45 50
Total 15 85 100
22. (2) Joint probability: the probability of an event
possessing two characteristics at the same time.
no. of occurrence possessing A and B
P(A and B) =
Grand total
P(male and E+)= 10 / 100
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Eye Glass
wearing
Eye Glass
not wearing
Total
Male 10 40 50
Female 5 45 50
Total 15 85 100
23. (3) Conditional probability: the probability of an event
occurring given that another event has occurred.
P(AB) = P(A ∩ B) / P(B)
= no. of occurrence possessing A and B / marginal total B
P(male ∩ E+) 10/100
P(maleE+) = = = 0.67
P(E+) 15/100
P(male ∩ E+) 10/100
P(E+male) = = = 0.2
P(male) 50/100
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Eye Glass
wearing
Eye Glass
not wearing
Total
Male 10 40 50
Female 5 45 50
Total 15 85 100
