Day 1 Notes
Probability
is the measure of how likely an
event is (written as a ratio)
Probability of an Probability of an eventevent
The number of ways the event can occur divided by the total number of possible outcomes
P(A) = The number of ways an event can occur
Total number of possible outcomes
P(odd) =
Example#1: You roll a six-sided die whose sides are numbered from 1 through 6. a) What is the probability of rolling an ODD number?
36
.5
P(“t”) =
b) What is the probability of rolling a number that starts with the letter “t”?
26
.33
Example #2: A jar contains 6 red, 5 green, 8 blue and 3 yellow marbles.
P(red) =
P(green) = P(blue) = P(yellow) =
622
522
822
322
.27
.23 .36 .14
Example#2: A jar contains 6 red, 5 green, 8 blue and 3 yellow marbles.
P(orange) = 0 0
Example #3: A deck of cards contains 52 cards made up of 4 different suits – Hearts, Diamonds, Spades, and Clubs.
a) What is the probability of drawing a heart?
13
P Heart52
.25
b) What is the probability of drawing a 3?
c) What is the probability of drawing a face card?
4
P a 352
.08
12
P face52
.23
Practice #4 The table gives the handedness and eyedness of a randomly selected group of 100 people.
Right-Right-EyedEyed
Left-Left-EyedEyed
Right-Right-HandedHanded
57 31
Left-Left-HandedHanded
6 6
a) What is the probability of getting a left-handed person?
12100
.12
Right-Right-EyedEyed
Left-Left-EyedEyed
Right-Right-HandedHanded
57 31
Left-Left-HandedHanded
6 6b) What is the probability of getting
someone who is left-eyed?37
100
Practice #4 The table gives the handedness and eyedness of a randomly selected group of 100 people.
.37
c) What is the probability of getting someone who is left-handed and is also left-eyed?
Right-Right-EyedEyed
Left-Left-EyedEyed
Right-Right-HandedHanded
57 31
Left-Left-HandedHanded
6 6
6100
Practice #4 The table gives the handedness and eyedness of a randomly selected group of 100 people.
.06
d) What is the probability of getting someone who is right-handed and is also right-eyed?
Right-Right-EyedEyed
Left-Left-EyedEyed
Right-Right-HandedHanded
57 31
Left-Left-HandedHanded
6 6
57100
Practice #4 The table gives the handedness and eyedness of a randomly selected group of 100 people.
.57
You Try!!
e)
f) 31100
.31
.8888100
Practice #5The chart shows favorite subjects of students based on their gender.
MathMath SciencSciencee
EnglisEnglishh
SSSS
MaleMale 46 42 13 25FemalFemalee
12 21 45 36
a) What is the probability that a randomly chosen student likes Social Studies the most?
61240
.25
MathMath SciencSciencee
EnglisEnglishh
SSSS
MaleMale 46 42 13 25FemalFemalee
12 21 45 36
b) What is the probability that a randomly chosen student is female?
Practice #5The chart shows favorite subjects of students based on their gender.
.475114240
MathMath SciencSciencee
EnglisEnglishh
SSSS
MaleMale 46 42 13 25FemalFemalee
12 21 45 36c) What is the probability that a
randomly chosen student both likes science and is a male?
Practice #5The chart shows favorite subjects of students based on their gender.
.17542240
MathMath SciencSciencee
EnglisEnglishh
SSSS
MaleMale 46 42 13 25FemalFemalee
12 21 45 36d) What is the probability that a
randomly chosen student likes social studies and is a female?
Practice #5The chart shows favorite subjects of students based on their gender.
.1536240
You Try!!
e)
f) 45240
.1875
.2458240
Day 2 Notes
Probability TablesProbability Tables
A Little Vocabulary Athletics
Music/Arts
SGA Other Total
Male Male total
Female Female
total
Total Athletics
totalMusic/arts
totalSGA total
Other total
Table total
Joint Probability
individual celltable total
Marginal Probability
column or row totaltable total
Conditional Probability
individual cellspecified row or column
Example 1•Using the table below, what is
the joint probability of a female that is involved in SGA?
Athletics
Music/Arts
SGA Other Total
Male 10 5 1 2 18 Femal
e5 6 0 1 12
Total 15 11 1 3 30
0/30 = 0
Example 2•Using the table below, what is
the marginal probability of choosing someone who is involved with athletics?
Athletics
Music/Arts
SGA Other Total
Male 10 5 1 2 18 Femal
e5 6 0 1 12
Total 15 11 1 3 30
15/30 = .50
Example 3•Using the table below, what is
the conditional probability given that a person is male, that they are involved in Music/Arts?
Athletics
Music/Arts
SGA Other Total
Male 10 5 1 2 18 Femal
e5 6 0 1 12
Total 15 11 1 3 30
5/18 = .28
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