Let S be a sample space and E and F be events associated with S . Suppose that Pr ( E ) = .6 , Pr ( F ) = .3 , and Pr ( E ∩ F ) = .2 . Calculate a. Pr ( E | F ) b. Pr ( F | E ) c. Pr ( E | F ′ ) d. Pr ( E ′ | F ′ ) .
Let S be a sample space and E and F be events associated with S . Suppose that Pr ( E ) = .6 , Pr ( F ) = .3 , and Pr ( E ∩ F ) = .2 . Calculate a. Pr ( E | F ) b. Pr ( F | E ) c. Pr ( E | F ′ ) d. Pr ( E ′ | F ′ ) .
Solution Summary: The author calculates the value of Pr(E|F) if the sample space is S and the events are E and F.
Let S be a sample space and E and F be events associated with S. Suppose that
Pr
(
E
)
=
.6
,
Pr
(
F
)
=
.3
,
and
Pr
(
E
∩
F
)
=
.2
. Calculate
a.
Pr
(
E
|
F
)
b.
Pr
(
F
|
E
)
c.
Pr
(
E
|
F
′
)
d.
Pr
(
E
′
|
F
′
)
.
Definition Definition For any random event or experiment, the set that is formed with all the possible outcomes is called a sample space. When any random event takes place that has multiple outcomes, the possible outcomes are grouped together in a set. The sample space can be anything, from a set of vectors to real numbers.
Please solve the following Probability Problem, please show all work and solve what is asked:
HW 1.w. (Special game)The atmosphere has heated up and a fight erupted! There are n + 1players and somebody threw the first punch. Once a person is punched,they punch another person in the group at random. What are the oddsthat after m iterations:a) Nobody punches the person who started it?b) Nobody gets punched twice?Now take it up a notch: imagine the first person punched N other peopleat random, and once someone gets punched, they punch another N peoplein the group at random, and so on. Again, what are the odds that afterm iterations:a) Nobody punches the person who started it?b) Nobody gets punched twice?
Q1. A chest of drawers has 3 drawers. Each drawer has 2 boxes. The boxes of one
drawer contain a silver coin in each respectively, the boxes of another a gold coin in
each box, and the boxes of the third drawer a gold and a silver coin, respectively. A
drawer is selected at random and a box from the drawer is selected at random and
opened. The coin is found to be silver. What is the probability that the coin in the
other box is gold? (Harder Problem)
Write codes to perform the functions in each of these cases
i.
ii.
Apply cd command to tell STATA the filepath associated with
your "favorite folder" (use the same name for the favorite folder
that we have been using in class)
Apply log using command to tell stata that you are creating a log
file to record the codes and the outcomes of these codes. Make
sure your log file is called loghwa1_W25.smcl. Do not forget to
include the replace option.
iii. Get help for the "regress" command & include a screenshot of
the outcome of this code
iv.
V.
Open a stata file stored in STATA memory called pop2000.dta
Continue from question iv. Save this file in your favorite folder
(current working directory) using a different name & a replace
option
Chapter 6 Solutions
Finite Mathematics & Its Applications (12th Edition)
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Probability & Statistics (28 of 62) Basic Definitions and Symbols Summarized; Author: Michel van Biezen;https://www.youtube.com/watch?v=21V9WBJLAL8;License: Standard YouTube License, CC-BY
Introduction to Probability, Basic Overview - Sample Space, & Tree Diagrams; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=SkidyDQuupA;License: Standard YouTube License, CC-BY