Suppose the urn has 7 red balls and 3 black balls initially, as before; but now...
Suppose the urn has 7 red balls and 3 black balls initially, as before; but now suppose that at each draw the color of the ball drawn is noted and the ball is replaced in the urn, together with another ball of the same color. Are the draws independent? Find P(R1),P(R2),and P(R3).
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Suppose the urn has 7 red balls and 3 black balls initially, as
before; but now...
this is the last problem. 6. A jar contains 5 red balls and 5 black balls....
this is the last problem. 6. A jar contains 5 red balls and 5 black balls. Two balls are successively drawn from the jar. After the first draw the color of the ball is noted, and then the selected ball is returned to the jar together with another ball of the opposite color. In other words, if a red ball is drawn it is returned to the jar together with another black ball; if black ball is drawn it is...
2. An urn contains two green balls and three red balls. Suppose two balls will be...
2. An urn contains two green balls and three red balls. Suppose two balls will be drawn at random one after another and without replacement (i.e., the first ball is not returned to the urn before the second one is drawn). (a) Find the probabilities of the events A-I A green ball appears in the irst draw (Note, in event B, the first draw is supposed unknown, for example, after the first draw,you do not look at what color the...
Suppose that there are 2 red balls, 1 blue ball, and 2 white balls in an...
Suppose that there are 2 red balls, 1 blue ball, and 2 white balls in an urn. A ball is drawn and its color is noted. After the ball is drawn, it is set aside and is replaced with a blue ball. Another ball is then drawn from the urn. Find the probability the first ball drawn was red given that the second ball drawn was blue.
An urn initially contains r red balls and s black balls. A ball is selected at random but not rem...
An urn initially contains r red balls and s black balls. A ball is selected at random but not removed and a balls of the same color as the selection are added to the urn. The process is then repeated with a balls of one color or the other added to the urn at each epoch. With each addition the population of the urn increases by a and it is helpful to imagine that the (a) What is the probability...
3.14. An urn initially contains 5 white and 7 black balls. Each time a ball is...
3.14. An urn initially contains 5 white and 7 black balls. Each time a ball is selected, its color is noted and it is replaced in the urn along with 2 other balls of (a) the first 2 balls selected are black and the next 2 are white (b) of the first 4 balls selected, exactly 2 are black.
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...
Urn one contains two red, one black balls, urn two contains one red, three black balls,...
Urn one contains two red, one black balls, urn two contains one red, three black balls, and urn three contains one red, one black balls. A student chooses urn one or urn two at random, and selects one ball from the chosen urn at random and transfers it into urn three. Then he draws a ball from urn three. Given that the ball he draws is red, what is the probability that the transferred ball is red?
There are 7 black balls and 9 red balls in an urn. If 3 balls are...
There are 7 black balls and 9 red balls in an urn. If 3 balls are drawn without replacement, what is the probability that exactly 1 black ball is drawn? Express your answer as a fraction or a decimal number rounded to four decimal places.
An urn contains 7 white, 3 red and 10 black balls. If five balls are drawn...
An urn contains 7 white, 3 red and 10 black balls. If five balls are drawn at random, find the probability that at least one red ball is selected.
2. An urn contains two green balls and three red balls. Suppose two balls will be drawn at random one after another and without replacement (i.e., the first ball is not returned to the urn before the second one is drawn). (a) Find the probabilities of the events A-I A green ball appears in the irst draw (Note, in event B, the first draw is supposed unknown, for example, after the first draw,you do not look at what color the...
An urn initially contains r red balls and s black balls. A ball is selected at random but not removed and a balls of the same color as the selection are added to the urn. The process is then repeated with a balls of one color or the other added to the urn at each epoch. With each addition the population of the urn increases by a and it is helpful to imagine that the (a) What is the probability...
3.14. An urn initially contains 5 white and 7 black balls. Each time a ball is selected, its color is noted and it is replaced in the urn along with 2 other balls of (a) the first 2 balls selected are black and the next 2 are white (b) of the first 4 balls selected, exactly 2 are black.
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...
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