Let S be a sample space and E and F be events associated with S . Suppose that Pr ( E ) = 1 2 , Pr ( F ) = 1 3 , and Pr ( E ∪ F ) = 7 12 . Calculate a. Pr ( E ∩ F ) b. Pr ( E | F ) c. Pr ( F | E ) .
Let S be a sample space and E and F be events associated with S . Suppose that Pr ( E ) = 1 2 , Pr ( F ) = 1 3 , and Pr ( E ∪ F ) = 7 12 . Calculate a. Pr ( E ∩ F ) b. Pr ( E | F ) c. Pr ( F | E ) .
Let S be a sample space and E and F be events associated with S. Suppose that
Pr
(
E
)
=
1
2
,
Pr
(
F
)
=
1
3
,
and
Pr
(
E
∪
F
)
=
7
12
. Calculate
a.
Pr
(
E
∩
F
)
b.
Pr
(
E
|
F
)
c.
Pr
(
F
|
E
)
.
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.
Game: dropping marbles from a 100-floor tower, given unlimited amount of identical marbles.
if marble breaks when dropped from level X -> it breaks from all levels higher than X
if marble doesn't break when dropped from level Y -> no marbles will break when dropped from level lower than Y
Goal of Game: Find the highest level, from which the marbles doesn't break.
Please design a testing plan to minimize the worst-case number-of-tests required to find the answer, with the constraint you
can only break max 2 marbles.
What is the minimum number of tests required? Explain your testing plan and how you arrived at this number.
Height = 1
Width=1
How much is the shaded area in the chart above?
(a) Given z = x + jy determine if f (z) = z4 is analytic.(b) On an Argand Diagram sketch the region |z| < 1.(c) Map the region |z| < 1 into the function plane f (z) = U + jV , defined as f (z) = z4.
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