Let S be a sample space and E and F be events associated with S . Suppose that Pr ( E ) = 1 3 , Pr ( F ) = 5 12 , and Pr ( E ∪ F ) = 2 3 . 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 3 , Pr ( F ) = 5 12 , and Pr ( E ∪ F ) = 2 3 . Calculate a. Pr ( E ∩ F ) b. Pr ( E | F ) c. Pr ( F | E ) .
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 S. Suppose that
Pr
(
E
)
=
1
3
,
Pr
(
F
)
=
5
12
,
and
Pr
(
E
∪
F
)
=
2
3
. 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.
Find the inverse of the matrix, or determine that the inverse does not exist for:
€
(b)
7
-12
240
1 1 1
(c)
2 3 2
2 17
036
205
20
(d) -1
1
2
1
T NO
1
0
-1
00
1
0
02
(e)
1
0
00
0
0
1
1
4. Prove the following. Use full sentences. Equations in the middle of sentences are fine, but do
not use logical symbols.
(a)
(b)
(n+3)2 is odd for every even integer n.
It is not the case that whenever n is an integer such that 9 | n² then 9 | n.
3. (a)
(b)
Prove the following logical argument using the rules of inference. Do not make
use of conditional proof.
Vx(J(x)O(x))
3x(J(x) A¬S(x))
.
·.³x(O(x) ^ ¬S(x))
Rewrite the proof using full sentences, avoiding logical symbols. It does not
need to mention the names of rules of inference, but a fellow CSE 16 student should be
able to understand the logical reasoning.
Chapter 6 Solutions
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