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Chapter 2: Probability Section 2.3: Events

The document discusses probability and events. It defines an event as a subset of the sample space. It provides examples of experiments with sample spaces and possible events, such as rolling dice or tossing coins. It also discusses concepts like the complement of an event, mutually exclusive events, and Venn diagrams. It provides several examples analyzing the probability of different events and drawing Venn diagrams to visualize the relationships between events.

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33 views8 pages

Chapter 2: Probability Section 2.3: Events

The document discusses probability and events. It defines an event as a subset of the sample space. It provides examples of experiments with sample spaces and possible events, such as rolling dice or tossing coins. It also discusses concepts like the complement of an event, mutually exclusive events, and Venn diagrams. It provides several examples analyzing the probability of different events and drawing Venn diagrams to visualize the relationships between events.

Uploaded by

thermopolis3012
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as DOCX, PDF, TXT or read online on Scribd
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Chapter 2: Probability

Section 2.3: Events


Event: A subset of the sample space.
Consider rolling a red die and green die.
See figure 2.1 on p. 27
The sample space could be considered as a set of the sample points.
These could be represented by ordered pairs.
Some possible events:
A: both die show the same number of dots.
B: The sum of both die is even.


Find the sample space for the experiment of tossing a coin three times or
tossing three coins.






A: two heads
B: at least two heads
C: no heads
D: 3 tails.

P(A) = __________

P(B) = ___________

P(C) = ___________

P (D) = ____________

Suppose A is a subset of sample space S.
The complement of A is A, the set of elements not included in but in S.
A A = ________
A A = ________
P (A) + P (A) = _________
P (A) = _____________
P (A) = ____________
Two events are said to be mutually exclusive if they no outcomes in
common.
For rolling two dice when events are mutually exclusive.
A: Rolling an 8
B: Rolling an odd number
C: Rolling the same number on each die
D: Rolling a sum of at most 5
E: Rolling a 4




A and B are mutually exclusive events. P(A) = 0.3 and P(B) = 0.5.
1. P(A B) = ____________________





2. P(A) = _________________






3. P[(A B)] = ________________


Venn Diagrams

Mr. Valk is responsible for advising 94 freshmen. Sixty-two of the
students are taking English and 70 of the students are taking
mathematics. Forty seven of the students are taking both English
and mathematics courses.

a. Draw the Venn diagram.













b. What is the probability of randomly choosing a student who is
taking English but not mathematics?








c. What is the probability of randomly choosing a student who is
taking neither English nor mathematics courses?

2.72.
Ride Probability
Jungle Cruise (J) 0.74
Monorail (M) 0.70
Matterhorn (H) 0.62
J and M 0.52
J and H 0.46
M and H 0.44
J, M, and H 0.34

Draw the Venn diagram.












1. Find the probability that s/he will go on at least one ride.










2. Find the probability that s/he will not go on any of these rides


3. P (J M) = ______________






4. P[(J M)(MH)] = ______________







5. P(J MH) = _________________

Know the results from exercises 2.1 through 2.4.

Show: P[ (A B) (A B)] < P( A B)

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