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Lecture 7

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University of California - San Diego

Mathematics

MATH 11

David James Quarfoot

Spring

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4/17/17 Lecture Notes (7)
Friday, April 21, 2017
12:58 PM
• If P (A or B)= P(A) + P(B), if A and B are disjoint
P (A and B) = P(A)xP(B), if A and B are independent
Losing Disjointness!
More General Rule:
P(A or B) = P(A) + P(B) - P(A and B)
If so if
•it In probability class, "A or B" includes three ideas: 1) A, but not B, 2) B, but not A, 3) both A and B
In everyday speech, "A or B" can mean this same thing ["inclusive or"], or sometimes it means just two
ideas 1) A, but not B, 2) B, but not A ["exclusive or"]
Ex. Coffee or tea?
Example: 80% of college students like learning. 70% of college students like video games. 62% like both
learning and video games. What percent like learning or video games?
Let L be the event that a college student likes learning
Let V be the event that a college student likes video games
P(L or V) = P(L) + P(V) - P(L and V)
= 0.8 +0.7 - 0.62 =0.88
0.62 0.12
Describe the words the zone given by:
0.18: People who like learning but not video games
0.08 + 0.62 : People who like video games
0.12: People who dislike learning and video games
0.18 + 0.08 : People who like learning or video games but not both.
Contingency Tables: A Venn diagram alternative
H Like Video games Dislike video games Margin totals
Like learning 0.62 0.18 0.80
Dislike learning 0.08 0.12 0.20
Margin totals 0.70 0.30 1.00
Joint probability: the probability of two things joining forces an happening simultaneously. For example,
8% of students hold the joint opinion that learning is boring and video games are fun
Marginal Probabilities: the probability of one value of a categorical variable occurring, for example 80%
of students like learning,. These values are the sum of the joint probabilities in a row or column.
A harder example
A teacher surveys the class about Twitter and Instagram use. Of the students, 20 use both, 10 use
neither, 72 don’t use Instagram, and 38 don’t use Twitter. What is the probability that randomly chosen
student will be on Instagr

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