An urn has 12 red balls and 8 green balls. Pick 5, with replacement. What is...
An urn has 12 red balls and 8 green balls. Pick 5, with replacement. What is the probability of P(3R,2B)?
-I understand how to do the problem however I do not get how we can figure out the total # of events is going to be 20^5
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An urn has 12 red balls and 8 green balls. Pick 5, with
replacement. What is...
1. An urn contains 4 red balls, 3 black balls and 2 green balls. We draw...
1. An urn contains 4 red balls, 3 black balls and 2 green balls. We draw two balls at random (without replacement). If at least one of the two balls is red, we draw one more ball and stop. Otherwise, we draw two more balls without replacement. (i) Compute the probability that the last bal is red (NOTE that for this entire question, your notation is at least as impor tant as your final numerical answer. So, for example, do...
Exercise 1.49. An urn has n 3 green balls and 3 red balls. Draw&balls with replacement....
Exercise 1.49. An urn has n 3 green balls and 3 red balls. Draw&balls with replacement. Let B denote the event that a red ball is seen at least once. Find P(B) using the following methods. (a) Use inclusion-exclusion with the events Ai = {ith draw is red) Hint. Use the general inclusion-exclusion formula from Fact 1.26 and the binomial theorem from Fact D.2 (b) Decompose the event by considering the events of seeing a red ball exactly k times,...
An urn contains four red balls, two green balls, and three yellow balls. Three balls will...
An urn contains four red balls, two green balls, and three yellow balls. Three balls will be drawn from the urn, one at a time, at random. If the balls are drawn without replacement, what is the probability that the first is red, the second is green, and the third is yellow? If the balls are drawn with replacement, what is the probability the first is red, the second is green, and the third is yellow?
An urn contains 10 red balls. 7 green balls and 4 yellow balls. At random, 5...
An urn contains 10 red balls. 7 green balls and 4 yellow balls. At random, 5 balls are drawn (without replacement). What is the probability 3 of them are red?
An urn contains 5 blue balls, 5 white balls, 5 red balls, and 5 green balls....
An urn contains 5 blue balls, 5 white balls, 5 red balls, and 5 green balls. Larry is selecting 4 balls at random one after the other without replacement. What is the probability that at least one of the selected balls is blue?
(a) (2 pts) An urn contains 3 red and 5 green balls. At each step of...
(a) (2 pts) An urn contains 3 red and 5 green balls. At each step of this game, we pick one ball at random, note its color and return the ball to the urn together with anoter ball of the same color. Prove by induction that the probability that the ball we pick a red ball at the n-th step is 3/8.
(a) (2 pts) An urn contains 3 red and 5 green balls. At each step of...
(a) (2 pts) An urn contains 3 red and 5 green balls. At each step of this game, we pick one ball at random, note its color and return the ball to the urn together with anoter ball of the same color. Prove by induction that the probability that the ball we pick a red ball at the n-th step is 3/8.
(a) (2 pts) An urn contains 3 red and 5 green balls. At each step of...
(a) (2 pts) An urn contains 3 red and 5 green balls. At each step of this game, we pick one ball at random, note its color and return the ball to the urn together with anoter ball of the same color. Prove by induction that the probability that the ball we pick a red ball at the n-th step is 3/8.
Exercise 1.49. An urn has n -3 green balls and 3 red balls. Draw (balls with...
Exercise 1.49. An urn has n -3 green balls and 3 red balls. Draw (balls with replacement. Let B denote the event that a red ball is seen at least once. FindP) using the following methods. (a) Use inclusion-exclusion with the events /h dra is re Hint. Use the general inclusion-exclusion formula from Fact 12 and the binomial theorem from Fact D.2. (b) Decompose the event by considering the events of seeing a red ball exactly k times, with k...
1. From an urn, 10 balls with replacement are selected, the urn contains 14 white balls...
1. From an urn, 10 balls with replacement are selected, the urn contains 14 white balls and 5 red balls. Calculate the probability that less than 3 red balls have come out. 2. From an urn, 10 balls are selected with replacement, the urn contains 14 white balls and 14 red balls. Calculate the probability that at least 3 red balls have come out. 3. From an urn 5 balls without replacement are selected, the urn contains 11 balls, of...
1. An urn contains 4 red balls, 3 black balls and 2 green balls. We draw two balls at random (without replacement). If at least one of the two balls is red, we draw one more ball and stop. Otherwise, we draw two more balls without replacement. (i) Compute the probability that the last bal is red (NOTE that for this entire question, your notation is at least as impor tant as your final numerical answer. So, for example, do...
Exercise 1.49. An urn has n 3 green balls and 3 red balls. Draw&balls with replacement. Let B denote the event that a red ball is seen at least once. Find P(B) using the following methods. (a) Use inclusion-exclusion with the events Ai = {ith draw is red) Hint. Use the general inclusion-exclusion formula from Fact 1.26 and the binomial theorem from Fact D.2 (b) Decompose the event by considering the events of seeing a red ball exactly k times,...
(a) (2 pts) An urn contains 3 red and 5 green balls. At each step of this game, we pick one ball at random, note its color and return the ball to the urn together with anoter ball of the same color. Prove by induction that the probability that the ball we pick a red ball at the n-th step is 3/8.
(a) (2 pts) An urn contains 3 red and 5 green balls. At each step of this game, we pick one ball at random, note its color and return the ball to the urn together with anoter ball of the same color. Prove by induction that the probability that the ball we pick a red ball at the n-th step is 3/8.
(a) (2 pts) An urn contains 3 red and 5 green balls. At each step of this game, we pick one ball at random, note its color and return the ball to the urn together with anoter ball of the same color. Prove by induction that the probability that the ball we pick a red ball at the n-th step is 3/8.
Exercise 1.49. An urn has n -3 green balls and 3 red balls. Draw (balls with replacement. Let B denote the event that a red ball is seen at least once. FindP) using the following methods. (a) Use inclusion-exclusion with the events /h dra is re Hint. Use the general inclusion-exclusion formula from Fact 12 and the binomial theorem from Fact D.2. (b) Decompose the event by considering the events of seeing a red ball exactly k times, with k...
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