(a) To define: The conditional probability of E given F and explain the way the probability is calculated.

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Answer 1

Question

Chapter 9, Problem 7CC

To determine

(a)

To define:

The conditional probability of E given F and explain the way the probability is calculated.

To determine

(b)

To define:

The independent events.

To determine

(c)

To explain:

The probability of occurrence of E and F if the events are independent and if the events are not independent.

To determine

(d)

To find:

The probability for occurrence of the event E and F together such that the balls are drawn with replacement. Also, find the probability if the balls are drawn without replacement.

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Simply:(p/(x-a))-(p/(x+a))

Q1lal Let X be an arbitrary infinite set and let r the family of all subsets F of X which do not contain a particular point x, EX and the complements F of all finite subsets F of X show that (X.r) is a topology. bl The nbhd system N(x) at x in a topological space X has the following properties NO- N(x) for any xX N1- If N EN(x) then x€N N2- If NEN(x), NCM then MeN(x) N3- If NEN(x), MEN(x) then NOMEN(x) N4- If N = N(x) then 3M = N(x) such that MCN then MeN(y) for any уем Show that there exist a unique topology τ on X. Q2\a\let (X,r) be the topology space and BST show that ẞ is base for a topology on X iff for any G open set xEG then there exist A Eẞ such that x E ACG. b\Let ẞ is a collection of open sets in X show that is base for a topology on X iff for each xex the collection B, (BEB\xEB) is is a nbhd base at x. - Q31 Choose only two: al Let A be a subspace of a space X show that FCA is closed iff F KOA, K is closed set in X. الرياضيات b\ Let X and Y be two topological space and f:X -…

Q1\ Let X be a topological space and let Int be the interior operation defined on P(X) such that 1₁.Int(X) = X 12. Int (A) CA for each A = P(X) 13. Int (int (A) = Int (A) for each A = P(X) 14. Int (An B) = Int(A) n Int (B) for each A, B = P(X) 15. A is open iff Int (A) = A Show that there exist a unique topology T on X. Q2\ Let X be a topological space and suppose that a nbhd base has been fixed at each x E X and A SCX show that A open iff A contains a basic nbdh of each its point Q3\ Let X be a topological space and and A CX show that A closed set iff every limit point of A is in A. A'S A ACA Q4\ If ẞ is a collection of open sets in X show that ẞ is a base for a topology on X iff for each x E X then ẞx = {BE B|x E B} is a nbhd base at x. Q5\ If A subspace of a topological space X, if x Є A show that V is nbhd of x in A iff V = Un A where U is nbdh of x in X.

Answer 2

Question

Chapter 9, Problem 7CC

To determine

(a)

To define:

The conditional probability of E given F and explain the way the probability is calculated.

To determine

(b)

To define:

The independent events.

To determine

(c)

To explain:

The probability of occurrence of E and F if the events are independent and if the events are not independent.

To determine

(d)

To find:

The probability for occurrence of the event E and F together such that the balls are drawn with replacement. Also, find the probability if the balls are drawn without replacement.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 3

Question

Chapter 9, Problem 7CC

To determine

(a)

To define:

The conditional probability of E given F and explain the way the probability is calculated.

To determine

(b)

To define:

The independent events.

To determine

(c)

To explain:

The probability of occurrence of E and F if the events are independent and if the events are not independent.

To determine

(d)

To find:

The probability for occurrence of the event E and F together such that the balls are drawn with replacement. Also, find the probability if the balls are drawn without replacement.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 4

Question

Chapter 9, Problem 7CC

To determine

(a)

To define:

The conditional probability of E given F and explain the way the probability is calculated.

To determine

(b)

To define:

The independent events.

To determine

(c)

To explain:

The probability of occurrence of E and F if the events are independent and if the events are not independent.

To determine

(d)

To find:

The probability for occurrence of the event E and F together such that the balls are drawn with replacement. Also, find the probability if the balls are drawn without replacement.

Expert Solution & Answer

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Answer 5

Chapter 9, Problem 7CC

To determine

(a)

To define:

The conditional probability of E given F and explain the way the probability is calculated.

To determine

(b)

To define:

The independent events.

To determine

(c)

To explain:

The probability of occurrence of E and F if the events are independent and if the events are not independent.

To determine

(d)

To find:

The probability for occurrence of the event E and F together such that the balls are drawn with replacement. Also, find the probability if the balls are drawn without replacement.

Answer 6

Chapter 9, Problem 7CC

To determine

(a)

To define:

The conditional probability of E given F and explain the way the probability is calculated.

Answer 7

Chapter 9, Problem 7CC

To determine

(a)

To define:

The conditional probability of E given F and explain the way the probability is calculated.

Answer 8

To determine

(b)

To define:

The independent events.

Answer 9

To determine

(b)

To define:

The independent events.

Answer 10

To determine

(c)

To explain:

The probability of occurrence of E and F if the events are independent and if the events are not independent.

Answer 11

To determine

(c)

To explain:

The probability of occurrence of E and F if the events are independent and if the events are not independent.

Answer 12

To determine

(d)

To find:

The probability for occurrence of the event E and F together such that the balls are drawn with replacement. Also, find the probability if the balls are drawn without replacement.

Answer 13

To determine

(d)

To find:

The probability for occurrence of the event E and F together such that the balls are drawn with replacement. Also, find the probability if the balls are drawn without replacement.

Answer 14

Expert Solution & Answer

Answer 15

Expert Solution & Answer

Answer 16

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Answer 17

Ch. 9.1 - The Fundamental Counting Principle says that if...Ch. 9.1 - The number of ways of arranging r objects form n...Ch. 9.1 - The number of ways of choosing r objects from n...Ch. 9.1 - True or False? In counting combinations, order...Ch. 9.1 - Evaluating Permutations and Combinations Evaluate...Ch. 9.1 - Evaluating Permutations and Combinations Evaluate...Ch. 9.1 - Prob. 7E Ch. 9.1 - Prob. 8E Ch. 9.1 - Prob. 9E Ch. 9.1 - Evaluating Permutations and Combinations Evaluate...

(a) To define: The conditional probability of E given F and explain the way the probability is calculated.

Solution Summary: The author explains the conditional probability of E given F and the way the probability is calculated.

Concept explainers

Videos

(a)

To define:

The conditional probability of E given F and explain the way the probability is calculated.

(b)

To define:

The independent events.

(c)

To explain:

The probability of occurrence of E and F if the events are independent and if the events are not independent.

(d)

To find:

The probability for occurrence of the event E and F together such that the balls are drawn with replacement. Also, find the probability if the balls are drawn without replacement.

Want to see the full answer?

Chapter 9 Solutions

(a) To define: The conditional probability of E given F and explain the way the probability is calculated.

Solution Summary: The author explains the conditional probability of E given F and the way the probability is calculated.

Concept explainers

Videos

(a) To define: The conditional probability of E given F and explain the way the probability is calculated.

(b) To define: The independent events.

(c) To explain: The probability of occurrence of E and F if the events are independent and if the events are not independent.

(d) To find: The probability for occurrence of the event E and F together such that the balls are drawn with replacement. Also, find the probability if the balls are drawn without replacement.

Want to see the full answer?

Chapter 9 Solutions

(a)

To define:

The conditional probability of E given F and explain the way the probability is calculated.

(b)

To define:

The independent events.

(c)

To explain:

The probability of occurrence of E and F if the events are independent and if the events are not independent.

(d)

To find:

The probability for occurrence of the event E and F together such that the balls are drawn with replacement. Also, find the probability if the balls are drawn without replacement.