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1. Consider an urn with 4 blue balls, 6 red balls, and 3 yellow balls. Suppose...
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?
3. There are 6 red and 4 blue balls inside an urn. Three balls are selected at random without replacement. Find the probability of the event that more red balls are selected.
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?
Consider an urn containing 6 red balls and 3 blue balls from which 3 balls are selected without replacement. What is the probability of selecting a red ball, if you select exactly one blue ball?
An urn contains 3 balls, 1 of which is red, 1 of which is yellow, and 1 of which is blue. Four balls are drawn with replacement from the urn. What is the probability that all 3 balls are seen in these 4 draws?
An urn contains 3 red balls and 7 yellow balls. Suppose we select two balls from the urn without replacement. A. Referring to no replacement, find the probability that one ball is red and one ball is yellow B. Referring to no replacement, find the probability that the first ball is yellow or the second ball is yellow
An urn contains 5 red balls, 4 green balls, and 2 yellow balls. Draw 3 balls with replacement (draw a ball, record the color, and put ball back before drwing again). What is the probability that your draw (a) consists of all red balls? (b) consists of all the same color? (c) consists of all different colors? (d) consists of at least one green ball? (e) consists of exactly two green balls and one red ball?
An urn contains 3 yellow balls and 9 red balls. We select 4 balls from the urn with replacement. Find the probability that at least one yellow ball is obtained.
A ball is taken at random from an urn containing 2 red balls and 3 blue balls. If the ball is red a fair coin is tossed three times. If the ball is blue non-fair coin is tossed three times; for this second coin the probability of heads is .6. In either case we count the number of heads in the three tosses and call that number X. (a) Compute the conditional probability that X-2 if it is known that...
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...