Suppose urn X has 3 red balls and 2 blue balls while urn Y has 3 red balls and 4 blue balls. A ball is drawn from urn X and then put into urn Y.
(a) If a blue ball was drawn from Y, what is the probability a blue ball was drawn from X? (b) If a blue ball was drawn from X, what is the probability a blue ball was drawn from Y?
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?
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...
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.
Urn One has 11 red balls and 8 blue balls. Urn Two has 10 red balls and 5 blue balls. An urn is selected at random and then a ball is selected from the selected urn at random. What is the probability that the ball selected is blue? State your answer to three places of decimal. Your Answer:
An urn contains 5 blue balls, 3 yellow balls and 2 red balls. Three balls are drawn without replacement. (i) What is the probability that all three balls are blue? (ii) What is the probability that two balls are blue and one ball is yellow? (iii) What is the probability that at least one of the balls is blue?
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?
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...
In an urn, there are 3 blue balls and 2 red balls. A ball is selected at random without replacement. Regardless of what color the first ball was, a blue ball is added to the urn (so there are a total of 5 balls in the urn now). Then a second ball is selected from the urn. a) What is the chance that the second ball selected from the urn is blue? b) Given that the second ball is blue,...
In an urn, there are 3 blue balls and 2 red balls. A ball is selected at random without replacement. Regardless of what color the first ball was, a blue ball is added to the urn (so there are a total of 5 balls in the urn now). Then a second ball is selected from the urn. a) What is the chance that the second ball selected from the urn is blue? b) Given that the second ball is blue,...