Problem 5. An urn contains4 red and 3 green balls. Two balls are drawn randomly. a....
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.
An urn contains 5 red balls and 2 green balls. Two balls are drawn one after the other with replacement. What is the proba- bility that the second ball is red?
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?
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?
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?
A bowl contains 5 blue balls, 3 red balls and 2 green balls. If two balls are drawn successively at random without replacement, what is the probability of: (a) drawing a red ball on each of the two draws? (b) drawing a red ball on the second draw? (c) drawing a red ball on at least one of the two draws? (d) red on the first draw and blue on the second draw? (e) blue on the first draw given...
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...
1. We draw randomly without replacement 3 balls from an urn that contains 3 red and 5 white balls. Denote by X the number of red balls drawn. Find the probability distribution of X, its expected value, and its standard deviation.
Three balls are randomly drawn from an urn that contains four white and seven red balls. (a) What is the probability of drawing a red ball on the third draw? (Round your answer to 3 decimal places.) (b) What is the probability of drawing a red ball on the third draw given that at least one red ball was drawn on the first two draws? (Round your answer to 3 decimal places.)
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...