An urn contains 5 red, 6 blue, and 8 green balls. A. if a set of...
An urn contains 5 red, 6 blue, and 8 green balls.
A. if a set of 3 balls is randomly selected, what is the probability that each of the balls will be the same color?
b. if a set of 3 balls is selected but each time a ball is drawn the color is noted and the ball returned, what is the probability the balls will be the same color?
Homework Answers
An urn contains 6 red, 9 green, and 11 blue balls. The following is repeated 3...
An urn contains 6 red, 9 green, and 11 blue balls. The following is repeated 3 times: a ball is selected from the urn at random and removed (called “sampling without replacement”). Give your answers to 3 significant digits. (a) What is the probability that all 3 selected balls are the same color? (b) What is the probability that all 3 selected balls are different colors? (c) Repeat part (a) assuming “sampling with replacement”. That is, the following is repeated...
1. An urn initially contains 6 red and 8 green balls. Each time a ball is...
1. An urn initially contains 6 red and 8 green balls. Each time
a ball is selected, its color is recorded, and it is replaced in
the urn along with 2 other balls of the same color. Compute the
probability that:
(a) The first 2 balls selected are green and the next 2 are
red?
(b) Of the first 4 balls selected, exactly 2 are green?
(c) If the second ball selected is green, what is the
probability that the...
Question 3. (exercise 3.11-13 in textbook) An urn contains r red balls and b blue balls....
Question 3. (exercise 3.11-13 in textbook) An urn contains r red balls and b blue balls. A ball is chosen at random from the urn, its color is noted, and it is returned together with d more balls of the same color. This is repeated indefinitely. What is the probability that (a) The second ball drawn is blue? (b) The first ball drawn is blue given that the second ball drawn is blue? (c) Let Bn denote the event that...
Question 3. (exercise 3.11-13 in textbook) An urn contains r red balls and b blue balls....
Question 3. (exercise 3.11-13 in textbook) An urn contains r red balls and b blue balls. A ball is chosen at random from the urn, its color is noted, and it is returned together with d more balls of the same color. This is repeated indefinitely. What is the probability that (a) The second ball drawn is blue? (b) The first ball drawn is blue given that the second ball drawn is blue? (c) Let Bn denote the event that...
An urn contains 3 red balls, 2 blue balls, and 5 white balls. A ball is...
An urn contains 3 red balls, 2 blue balls, and 5 white balls. A ball is selected and its color noted. Then it is replaced. A second ball is selected and its color noted. Find the probability of: Selecting 2 blue balls (round to 4 decimal places)
Urn A contains two red balls and eight blue balls. Urn B contains two red balls and ten green balls. Six balls are drawn...
Urn A contains two red balls and eight blue balls. Urn B contains two red balls and ten green balls. Six balls are drawn from urn A and four are drawn from urn B; in each case, each ball is replaced before the next one is drawn. What is the most likely number of blue balls to be drawn? What is the most likely number of green balls to be drawn?
Exercise 3 (SOA type). Urn I contains 10 balls: 4 red and 6 blue. Urn II...
Exercise 3 (SOA type). Urn I contains 10 balls: 4 red and 6 blue. Urn II contains 16 red balls and an unknown number of blue balls. A single ball is drawn from each urn. The probability that both balls are the same color is 0.44. What is the number of blue balls in urn II?
An urn contains 2 balls that are either red or blue. At each step a ball...
An urn contains 2 balls that are either red or blue. At each step a ball is randomly drawn and replaced with a new ball, having the same color w.p. 4/5, or different color w.p. 1/5. Find the probability that the 5th ball drawn is red, if you start with 2 red balls in the urn. Please explain step by step how the transition probability matrix is formed.
Urn 1 contains 3 red and 6 blue balls, and urn 2 contains 4 red and...
Urn 1 contains 3 red and 6 blue balls, and urn 2 contains 4 red and 3 blue balls. The urns are equally likely to be chosen. a) If a blue ball is drawn, what is the probability that it came from urn 1? b) If a red ball is drawn, what is the probability that it came from urn 2?
Urn A contains 5 green and 3 red balls, and urn B contains 2 green and...
Urn A contains 5 green and 3 red balls, and urn B contains 2 green and 6 red balls. One ball is drawn from urn A and transferred to Urn b. Then one ball is drawn from urn B and transferred to urn A. Let X=the number of green balls in urn A after this process. List the possible values for X and then find the entire probability distribution for X.
1. An urn initially contains 6 red and 8 green balls. Each time
a ball is selected, its color is recorded, and it is replaced in
the urn along with 2 other balls of the same color. Compute the
probability that:
(a) The first 2 balls selected are green and the next 2 are
red?
(b) Of the first 4 balls selected, exactly 2 are green?
(c) If the second ball selected is green, what is the
probability that the...
Question 3. (exercise 3.11-13 in textbook) An urn contains r red balls and b blue balls. A ball is chosen at random from the urn, its color is noted, and it is returned together with d more balls of the same color. This is repeated indefinitely. What is the probability that (a) The second ball drawn is blue? (b) The first ball drawn is blue given that the second ball drawn is blue? (c) Let Bn denote the event that...
Question 3. (exercise 3.11-13 in textbook) An urn contains r red balls and b blue balls. A ball is chosen at random from the urn, its color is noted, and it is returned together with d more balls of the same color. This is repeated indefinitely. What is the probability that (a) The second ball drawn is blue? (b) The first ball drawn is blue given that the second ball drawn is blue? (c) Let Bn denote the event that...
Exercise 3 (SOA type). Urn I contains 10 balls: 4 red and 6 blue. Urn II contains 16 red balls and an unknown number of blue balls. A single ball is drawn from each urn. The probability that both balls are the same color is 0.44. What is the number of blue balls in urn II?
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