This document provides an overview of a probability and statistics course, including the grading criteria, topics that will be covered like machine learning, probability in real life examples, key terminology, types of events, and how probability is used in programming. The course will cover sample space, events, counting sample points, and probability of an event. Assignments will make up 20% of the grade, with the midterm and final exam making up 30% and 40% respectively. Topics that will be discussed include random variables, empirical vs theoretical probability, independent and mutually exclusive events, and probability distributions. Examples are provided for calculating probabilities of different events.

1. Probability and Statistics
Week 1
Sample Space, Events, Counting Sample points, Probability of an Event
Dr. Ferdin Joe John Joseph

2. Join Canvas Portal
https://canvas.instructure.com/enroll/CTA4JH
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3. Grade Spit
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Attendance
10%
Mid Term
30%
Final Exam
40%
Assignments
20%
PERCENTAGE

4. Grade Criteria
Score Grade
85 – 100 A
75 – 84 B+
70 – 74 B
65 – 69 C+
60 – 64 C
55 – 59 D+
50 – 54 D
<50 F
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5. Machine Learning
Machine Learning is an interdisciplinary field in Data Science that uses
• statistics
• probability
• algorithms
to learn from data and provide insights which can be used to build
intelligent applications.
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6. From MSE - 202 Learn
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7. From MSE - 202 Learn
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8. Probability in Real Life
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9. Probability in Real Life
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10. Probability in Real Life
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11. Probability in Real Life
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12. Probability for Data Science
•Probability deals with predicting the likelihood of
future events, while statistics involves the
analysis of the frequency of past events.
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13. Terminologies
• Sample Space
• Event
• Counting Sample Points
• Probability of an Event
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14. Event
• An event is a set of outcomes of an experiment to which a probability
is assigned.
• E represents event
• P(E) is the probability that the event E occur.
• A situation where E might happen (success) or might not happen
(failure) is called a trial.
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15. Event
• Tossing a coin
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16. Event
• Rolling dice
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17. Event
• Pulling colored ball out of the bag
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18. Random Variable
• The variable that represents the outcome of an events is called a
random variable.
• Eg. Getting head or tail in tossing a coin
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19. Random variable in tossing a coin
• If we toss a coin, the chances for getting head or tail is 50-50
• The probability of getting head or tail is ½ or 50%
• Random variable range between 0 and 1
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20. Empirical Probability
• Also known as practical probability
• It is the number of times the event occurs divided by the total
number of incidents observed.
• If for ‘n’ trials and we observe ‘s’ successes, the probability of success
is s/n.
• Toss a coin 4 times. The outcome is H, H, H, T
• P(Head) =3/4=0.75
• P(Tail)=1/4=0.25
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21. Theoretical probability
• The number of ways the particular event can occur divided by the
total number of possible outcomes.
• A head can occur once and possible outcomes are two (head, tail).
The true (theoretical) probability of a head is 1/2.
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22. Exercise 1
A die is rolled, find the probability that an even number is obtained.
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23. Exercise 1
A die is rolled, find the probability that an even number is obtained.
Solution:
Let us first write the sample space S of the experiment.
S = {1,2,3,4,5,6}
Let E be the event "an even number is obtained" and write it down.
E = {2,4,6}
We now use the formula of the classical probability.
P(E) = n(E) / n(S) = 3 / 6 = 1 / 2
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24. Exercise 2
Two coins are tossed, find the probability that two heads are obtained.
Note: Each coin has two possible outcomes H (heads) and T (Tails).
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25. Exercise 2
Two coins are tossed, find the probability that two heads are obtained.
Note: Each coin has two possible outcomes H (heads) and T (Tails).
The sample space S is given by.
S = {(H,T),(H,H),(T,H),(T,T)}
Let E be the event "two heads are obtained".
E = {(H,H)}
We use the formula of the classical probability.
P(E) = n(E) / n(S) = 1 / 4
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26. Exercise 3
A card is drawn at random from a deck of cards. Find the probability of
getting the 3 of diamond.
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27. Exercise 3
A card is drawn at random from a deck of cards. Find the probability of
getting the 3 of diamond.
The sample space S of the experiment in question 6 is shown below
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28. Exercise 3
A card is drawn at random from a deck of cards. Find the probability of
getting the 3 of diamond.
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29. Exercise 3
A card is drawn at random from a deck of cards. Find the probability of
getting the 3 of diamond.
Let E be the event "getting the 3 of diamond". An examination of the
sample space shows that there is one "3 of diamond" so that n(E) = 1
and n(S) = 52. Hence the probability of event E occurring is given by
P(E) = 1 / 52
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30. Exercise 4
The blood groups of 200 people is distributed as follows:
50 have type A blood,
65 have B blood type,
70 have O blood type and
15 have type AB blood.
If a person from this group is selected at random, what is the
probability that this person has O blood type?
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31. Exercise 4
We construct a table of frequencies for the the blood groups as follows
group frequency
A 50
B 65
O 70
AB 15
We use the empirical formula of the probability
P(E) = Frequency for O blood / Total frequencies
= 70 / 200 = 0.35
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32. Classwork 1
What is the probability of throwing one dice and getting the number
greater than 4 ?
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33. Classwork 2
The customer wants to buy a bread and a can. There are 30 pieces of
bread in the shop, including 5 from the previous day, and 20 cans with
unreadable expiration date, of which one has expired. What is the
probability that the customer will buy a fresh bread and a tin under
warranty ?
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34. Classwork 3
What is the probability that if we choose a trinity from 19 boys and 12
girls, we will have :
a) three boys
b) three girls
c) two boys and one girl ?
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36. Types of Events
• Independent
• Mutually Exclusive
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37. Independent Events
• Two or more events not having control over the outcome of the
others.
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38. Mutually Exclusive Events
• If two events are NOT independent, then we say that they are dependent.
• Sampling may be done with replacement or without replacement.
• With replacement: If each member of a population is replaced after it is
picked, then that member has the possibility of being chosen more than
once. When sampling is done with replacement, then events are
considered to be independent, meaning the result of the first pick will not
change the probabilities for the second pick.
• Without replacement: When sampling is done without replacement, each
member of a population may be chosen only once. In this case, the
probabilities for the second pick are affected by the result of the first pick.
The events are considered to be dependent or not independent.
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39. Sampling with replacement
• Suppose you pick three cards with replacement. The first card you
pick out of the 52 cards is the
• Q of spades. You put this card back, reshuffle the cards and pick a
second card from the 52-card deck. It is the ten of clubs. You put this
card back, reshuffle the cards and pick a third card from the 52-card
deck. This time, the card is the Q of spades again. Your picks are {Q of
spades, ten of clubs, Q of spades}. You have picked the Q of spades
twice. You pick each card from the 52-card deck.
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40. Sampling without replacement
• Suppose you pick three cards without replacement. The first card you
pick out of the 52 cards is the
• K of hearts. You put this card aside and pick the second card from the
51 cards remaining in the deck. It is the three of diamonds. You put
this card aside and pick the third card from the remaining 50 cards in
the deck. The third card is the J of spades. Your picks are {K of hearts,
three of diamonds, J of spades}. Because you have picked the cards
without replacement, you cannot pick the same card twice.
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41. Probability Distribution
• A probability distribution is a list of all of the possible outcomes of a
random variable along with their corresponding probability values.
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42. Probability usage in programming
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43. Probability usage in programming
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# generate random floating point values
from random import seed
from random import random
# seed random number generator
seed(1)
# generate random numbers between 0-1
for _ in range(10):
value = random()
print(value)

44. Probability usage in programming
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# generate random integer values
from random import seed
from random import randint
# seed random number generator
seed(1)
# generate some integers
for _ in range(10):
value = randint(0, 10)
print(value)

45. Probability usage in programming
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# choose a random element from a list
from random import seed
from random import choice
# seed random number generator
seed(1)
# prepare a sequence
sequence = [i for i in range(20)]
print(sequence)
# make choices from the sequence
for _ in range(5):
selection = choice(sequence)
print(selection)

46. Probability usage in programming
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# randomly shuffle a sequence
from random import seed
from random import shuffle
# seed random number generator
seed(1)
# prepare a sequence
sequence = [i for i in range(20)]
print(sequence)
# randomly shuffle the sequence
shuffle(sequence)
print(sequence)

47. Slides Available in link below
www.slideshare.net/ferdinjoe
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