Day 1 Notes. Probability is the measure of how likely an event is (written as a ratio)
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Transcript of Day 1 Notes. Probability is the measure of how likely an event is (written as a ratio)
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Day 1 Notes
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Probability
is the measure of how likely an
event is (written as a ratio)
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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
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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
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P(“t”) =
b) What is the probability of rolling a number that starts with the letter “t”?
26
.33
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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
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Example#2: A jar contains 6 red, 5 green, 8 blue and 3 yellow marbles.
P(orange) = 0 0
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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
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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
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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
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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
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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
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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
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You Try!!
e)
f) 31100
.31
.8888100
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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
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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
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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
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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
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You Try!!
e)
f) 45240
.1875
.2458240
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Day 2 Notes
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Probability TablesProbability Tables
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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
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Joint Probability
individual celltable total
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Marginal Probability
column or row totaltable total
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Conditional Probability
individual cellspecified row or column
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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
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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
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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