Exercise 2.19. We have an urn with balls labeled 1,..., 7. Two balls are drawn. Let...
Exercise 2.19. We have an urn with balls labeled 1,..., 7. Two balls are drawn. Let X1 be the number of the first ball drawn and X2 the number of the second ball drawn. By counting favorable outcomes, compute the probabilities P(X 1 = 4), P(X2 = 5), and P(X1 = 4,X 2 = 5) in cases (a) and (b) below.
(a) The balls are drawn with replacement.
(b) The balls are drawn without replacement.
(c) Does the answer to either (a) or (b) prove something about the independence of the random variables X1 and X2?
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Exercise 2.19. We have an urn with balls labeled 1,..., 7. Two
balls are drawn. Let...
Problem 6 Probability + Counting (3x 3 x 2 18 pts) An urn A coutains tem labeled balls whie each ...
Problem 6 Probability + Counting (3x 3 x 2 18 pts) An urn A coutains tem labeled balls whie each label containsa tumber, rangleg from 2.to 10. An urn B contains five labeled balls while the 1.2,to 5 (a) Two balls are drawn, one froan A and one from B. What is the sample space? What is the probability thst the sum of the labels on the balls is odd? What is the probahility that the sam of the labels...
An urn contains 8 balls numbered 1-8 and a ball is randomly drawn from the urn....
An urn contains 8 balls numbered 1-8 and a ball is randomly drawn from the urn. Let A = “Ball number 2, 4 or 6 is chosen” and let B = “Ball number 3,4,5,6 or 7 is chosen”. Calculate the following probabilities: a)P(A) b) P(A') c) P(A∪B) d) P(A|B)
Suppose there is an urn containing 5 red, 4 white, and 11 blue balls. We drawn...
Suppose there is an urn containing 5 red, 4 white, and 11 blue balls. We drawn six balls from the urn (no replacement) (a) Find the number of ways (not the probability) of choosing a red ball, then a blue ball, then exactly 2 white balls, and finally exactly 2 blue balls. (b)Find the number of ways of choosing 2 red balls initially , then at least 3 blue balls, then a green ball. (c) Find the number of ways...
1. An urn contains balls numbered 1 through 7. A ball is drawn and replaced, and...
1. An urn contains balls numbered 1 through 7. A ball is drawn and replaced, and a second ball is drawn. a) How many outcomes are in the sample space? 7 different outcomes b) Describe the outcome "ball number 3 is drawn, then ball number 7 is drawn." a) How many outcomes are in the sample space? There is/are 7 differ Butcome(s) in the sample space. (Simplify your answer.) b) Describe the outcome "ball number 3 is drawn, then ball...
1.4-15. An urn contains 10 red and 10 white balls. The balls are drawn from the...
1.4-15. An urn contains 10 red and 10 white balls. The balls are drawn from the urn at random, one at a time. Find the probabilities that the fourth white ball is the fourth, fifth, sixth, or seventh ball drawn if the sampling is done (a) With replacement. (b) Without replacement. (c) In the World Series, the American League (red) and National League (white) teams play until one team wins four games. Do you think that the urn model pre-...
a-d 2. An urn contains 4 balls numbered 1,2,3,4, respectively. Two balls are drawn without replacement....
a-d
2. An urn contains 4 balls numbered 1,2,3,4, respectively. Two balls are drawn without replacement. Let A be the event that the first ball drawn has a 1 on it, and let B be the event tha the second ball has a 1 on it. a) Find P(BIA) b) Find P(B) c) If C is the event a 1 is drawn, find P(C). d) Find P(A IC)
a) Two balls are drawn without replacement from an urn containing 12 balls, of which 7...
a) Two balls are drawn without replacement from an urn containing 12 balls, of which 7 are white and 5 are black. Find the probability that: (i) Both balls will be white (ii) Both balls will be the same color (iii) At least one of the balls will be white b) Repeat part (a) but with the balls drawn with replacement
An urn contains 5 balls numbered 1 to 5. Two balls are drawn replacement Let X be the sum of the ...
An urn contains 5 balls numbered 1 to 5. Two balls are drawn replacement Let X be the sum of the two numbers drawn. (a). What are the possible values of X? (b). if let X be the subtraction of the two numbers drawn.What are the possible values of X? (c). if let X be the product of the two numbers drawn.What are the possible values of X? (d). if let X be the Quotient of the two numbers drawn.What...
Problem 5. An urn contains4 red and 3 green balls. Two balls are drawn randomly. a....
Problem 5. An urn contains4 red and 3 green balls. Two balls are drawn randomly. a. Let Z be the number of green balls when the draws are done without replacement. Give the possible values and the pmf of 2. b. Let W be the number of green balls when the draws are done with replacement. Give the possible values and the pmf of W.
An urn “A' contains 2 white and 4 black balls. Another urn ® contains 5 white and 7 black ball. A ball is transferred from the urn $A) to urn B'. Then a ball is drawn from urn B'. Find the probability, that it will be white.
An urn “A' contains 2 white and 4 black balls. Another urn ®contains 5 white and 7 black ball. A ball is transferred from the urn $A)to urn B'. Then a ball is drawn from urn B'. Find the probability, thatit will be white.
Problem 6 Probability + Counting (3x 3 x 2 18 pts) An urn A coutains tem labeled balls whie each label containsa tumber, rangleg from 2.to 10. An urn B contains five labeled balls while the 1.2,to 5 (a) Two balls are drawn, one froan A and one from B. What is the sample space? What is the probability thst the sum of the labels on the balls is odd? What is the probahility that the sam of the labels...
1. An urn contains balls numbered 1 through 7. A ball is drawn and replaced, and a second ball is drawn. a) How many outcomes are in the sample space? 7 different outcomes b) Describe the outcome "ball number 3 is drawn, then ball number 7 is drawn." a) How many outcomes are in the sample space? There is/are 7 differ Butcome(s) in the sample space. (Simplify your answer.) b) Describe the outcome "ball number 3 is drawn, then ball...
1.4-15. An urn contains 10 red and 10 white balls. The balls are drawn from the urn at random, one at a time. Find the probabilities that the fourth white ball is the fourth, fifth, sixth, or seventh ball drawn if the sampling is done (a) With replacement. (b) Without replacement. (c) In the World Series, the American League (red) and National League (white) teams play until one team wins four games. Do you think that the urn model pre-...
a-d
2. An urn contains 4 balls numbered 1,2,3,4, respectively. Two balls are drawn without replacement. Let A be the event that the first ball drawn has a 1 on it, and let B be the event tha the second ball has a 1 on it. a) Find P(BIA) b) Find P(B) c) If C is the event a 1 is drawn, find P(C). d) Find P(A IC)
Problem 5. An urn contains4 red and 3 green balls. Two balls are drawn randomly. a. Let Z be the number of green balls when the draws are done without replacement. Give the possible values and the pmf of 2. b. Let W be the number of green balls when the draws are done with replacement. Give the possible values and the pmf of W.
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