KONSEP DASAR PROBABILITAS

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KONSEP DASAR PROBABILITAS
STATISTIK DAN PROBABILISTIK

• BUDHI SETIAWAN
• TEKNIK SIPIL UNSRI

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Kondisi acak

• Kondisi acak adalah satu kondisi dimana hasil
  atau keadaan tidak dapat diprediksi

Contoh Status penyakit
Anda memiliki penyakit Anda tidak memiliki
penyakit Hasil test positif Hasil test negatif
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Definisi Probabilitas

• Probabilitas adalah nilai antara 0 dan 1 yang
  dituliskan dalam bentuk desimal ataupun pecahan.
• Secara sederhana, Probability adalah bilangan
  antara 0 dan 1 yang menunjukkan suatu hasil yang
  diperoleh dari kondisi acak.
• Untuk satu susunan kemungkinan yang lengkap dalam
  kondisi acak, maka total atau jumlah probabilitas
  adalah harus sama dengan 1.

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Assigning ProbabilityHow likely it is that a
particular outcome will be the result of a random
circumstance
The Relative Frequency Interpretation of
Probability
In situations that we can imagine repeating many
times, we define the probability of a specific
outcome as the proportion of times it would occur
over the long run -- called the relative
frequency of that particular outcome.
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Contoh Probabilitas dalam perencanaan
transportasi
Banyaknya Mobil Jumlah Pengamatan Frekuensi relative
0 4 4/60
1 16 16/60
2 20 20/60
3 14 14/60
4 3 3/60
5 2 2/60
6 1 1/60
7 0 0
8 0 0
. . .
Di suatu ruas jalan direncanakan untuk membuat
jalur khusus belok kanan. Probabilitas 5 mobil
menunggu berbelok diperlukan untuk menentukan
panjang garis pembagi jalan. Untuk keperluan ini
dilakukan survey selama 2 bulan dan diperoleh 60
hasil pengamatan.

• Probabilitas kejadian 5 mobil menunggu untuk
  berbelok kanan adalah 3/60 (2/60 1/60)

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Determining the Relative Frequency(Probability)
of an Outcome
Method 1 Make an Assumption about the Physical
World (there is no bias)
A Simple LotteryChoose a three-digit number
between 000 and 999. Player wins if his or her
three-digit number is chosen. Suppose the 1000
possible 3-digit numbers (000, 001, 002, 999) are
equally likely.In long run, a player should win
about 1 out of 1000 times. Probability 0.0001
of winning.This does not mean a player will win
exactly once in every thousand plays.
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Determining the Relative Frequency(Probability)
of an Outcome
Method 2 Observe the Relative Frequency of
random circumstances
The Probability of Lost Luggage1 in 176
passengers on U.S. airline carriers will
temporarily lose their luggage.This number is
based on data collected over the long run. So the
probability that a randomly selected passenger on
a U.S. carrier will temporarily lose luggage is
1/176 or about 0.006.
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Proportions and Percentages as Probabilities
Ways to express the relative frequency of lost
luggage

• The proportion of passengers who lose their
  luggage is 1/176 or about 0.006 (6 out of 1000).
• About 0.6 of passengers lose their luggage.
• The probability that a randomly selected
  passenger will lose his/her luggage is about
  0.006.
• The probability that you will lose your luggage
  is about 0.006.

Last statement is not exactly correct your
probability depends on other factors (how late
you arrive at the airport, etc.).
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Estimating Probabilities from Observed
Categorical Data
Assuming data are representative, the probability
of a particular outcome is estimated to be the
relative frequency (proportion) with which that
outcome was observed.Approximate margin of
error for the estimated probability is
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Nightlights and Myopia
Assuming these data are representative of a
larger population, what is the approximate
probability that someone from that population who
sleeps with a nightlight in early childhood will
develop some degree of myopia?
Note 72 7 79 of the 232 nightlight users
developed some degree of myopia. So we estimate
the probability to be 79/232 0.34. This
estimate is based on a sample of 232 people with
a margin of error of about 0.066 (1/v232
0.666)
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The Personal Probability Interpretation
Personal probability of an event the degree
to which a given individual believes the event
will happen. Sometimes subjective probability
used because the degree of belief may be
different for each individual.

• Restrictions on personal probabilities
• Must fall between 0 and 1 (or between 0 and
  100).
• Must be coherent.

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Probability Definitions and Relationships
Sample space collection of unique,
nonoverlapping possible outcomes of a random
circumstance. Simple event one outcome in the
sample space a possible outcome of a random
circumstance. Event a collection of one or more
simple events in the sample space often written
as A, B, C, and so on.
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Assigning Probabilities to Simple Events
P(A) probability of the event A

• Conditions for Valid Probabilities
• Each probability is between 0 and 1.
• The sum of the probabilities over all possible
  simple events is 1.

Equally Likely Simple EventsIf there are k
simple events in the sample space and they are
all equally likely, then the probability of the
occurrence of each one is 1/k.
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Example Probability of Simple Events
Random Circumstance A three-digit winning
lottery number is selected.Sample Space
000,001,002,003, . . . ,997,998,999. There
are 1000 simple events.Probabilities for Simple
Event Probability any specific three-digit
number is a winner is 1/1000. Assume all
three-digit numbers are equally likely.
Event A last digit is a 9 009,019, . . .
,999. Since one out of ten numbers in set, P(A)
1/10. Event B three digits are all the same
000, 111, 222, 333, 444, 555, 666, 777,
888, 999. Since event B contains 10 events,
P(B) 10/1000 1/100.