Let S be a sample space and E and F be events associated with. Suppose that Pr ( E ) = .4 , Pr ( F | E ) = .25 , and Pr ( F ) = .3 . Calculate a. Pr ( E ∩ F ) b. Pr ( E ∪ F ) c. Pr ( E | F ) d. Pr ( E ′ ∩ F ) .
Let S be a sample space and E and F be events associated with. Suppose that Pr ( E ) = .4 , Pr ( F | E ) = .25 , and Pr ( F ) = .3 . Calculate a. Pr ( E ∩ F ) b. Pr ( E ∪ F ) c. Pr ( E | F ) d. Pr ( E ′ ∩ F ) .
Solution Summary: The author calculates the value of Pr(Ecap 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. Suppose that
Pr
(
E
)
=
.4
,
Pr
(
F
|
E
)
=
.25
,
and
Pr
(
F
)
=
.3
. Calculate
a.
Pr
(
E
∩
F
)
b.
Pr
(
E
∪
F
)
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.
-
Let n = 7, let p = 23 and let S be the set of least positive residues mod p of the first (p − 1)/2
multiple of n, i.e.
n mod p, 2n mod p, ...,
p-1
2
-n mod p.
Let T be the subset of S consisting of those residues which exceed p/2.
Find the set T, and hence compute the Legendre symbol (7|23).
23
32
how come?
The first 11 multiples of 7 reduced mod 23 are
7, 14, 21, 5, 12, 19, 3, 10, 17, 1, 8.
The set T is the subset of these residues exceeding
So T = {12, 14, 17, 19, 21}.
By Gauss' lemma (Apostol Theorem 9.6),
(7|23) = (−1)|T| = (−1)5 = −1.
Let n = 7, let p = 23 and let S be the set of least positive residues mod p of the first (p-1)/2
multiple of n, i.e.
n mod p, 2n mod p, ...,
2
p-1
-n mod p.
Let T be the subset of S consisting of those residues which exceed p/2.
Find the set T, and hence compute the Legendre symbol (7|23).
The first 11 multiples of 7 reduced mod 23 are
7, 14, 21, 5, 12, 19, 3, 10, 17, 1, 8.
23
The set T is the subset of these residues exceeding
2°
So T = {12, 14, 17, 19, 21}.
By Gauss' lemma (Apostol Theorem 9.6),
(7|23) = (−1)|T| = (−1)5 = −1.
how come?
Shading a Venn diagram with 3 sets: Unions, intersections, and...
The Venn diagram shows sets A, B, C, and the universal set U.
Shade (CUA)' n B on the Venn diagram.
U
Explanation
Check
A-
B
Q Search
田
Chapter 6 Solutions
Finite Mathematics & Its Applications (12th Edition)
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.
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