An urn contains 5 red balls, 4 green balls, and 2 yellow balls. Draw 3 balls...
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?
Homework Answers
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An urn contains 5 red balls, 4 green balls, and 2 yellow balls.
Draw 3 balls...
An urn contains 1 green ball, 1 red ball, 1 yellow ball and 1 white ball....
An urn contains 1 green ball, 1 red ball, 1 yellow ball and 1 white ball. I draw 4 balls with replacement. What is the probability that there is at least one color that is appears exactly twice?
An urn contains 6 red, 9 green, and 11 blue balls. The following is repeated 3...
An urn contains 6 red, 9 green, and 11 blue balls. The following is repeated 3 times: a ball is selected from the urn at random and removed (called “sampling without replacement”). Give your answers to 3 significant digits. (a) What is the probability that all 3 selected balls are the same color? (b) What is the probability that all 3 selected balls are different colors? (c) Repeat part (a) assuming “sampling with replacement”. That is, the following is repeated...
10. There are 10 balls in an urn: 4 red, 3 green, 3 yellow. One randomly...
10. There are 10 balls in an urn: 4 red, 3 green, 3 yellow. One randomly takes 3 balls. What is the probability that (a) all of them are of different colors? b) all of them are of the same color? (c) two of them are red? (d) two of them are red and one of them is green?
An urn contains 5 blue balls, 3 yellow balls and 2 red balls. Three balls are...
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?
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 3 yellow balls and 9 red balls. We select 4 balls from the...
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.
1. An urn initially contains 6 red and 8 green balls. Each time a ball is...
1. An urn initially contains 6 red and 8 green balls. Each time
a ball is selected, its color is recorded, and it is replaced in
the urn along with 2 other balls of the same color. Compute the
probability that:
(a) The first 2 balls selected are green and the next 2 are
red?
(b) Of the first 4 balls selected, exactly 2 are green?
(c) If the second ball selected is green, what is the
probability that the...
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?
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...
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...
10. There are 10 balls in an urn: 4 red, 3 green, 3 yellow. One randomly takes 3 balls. What is the probability that (a) all of them are of different colors? b) all of them are of the same color? (c) two of them are red? (d) two of them are red and one of them is green?
1. An urn initially contains 6 red and 8 green balls. Each time
a ball is selected, its color is recorded, and it is replaced in
the urn along with 2 other balls of the same color. Compute the
probability that:
(a) The first 2 balls selected are green and the next 2 are
red?
(b) Of the first 4 balls selected, exactly 2 are green?
(c) If the second ball selected is green, what is the
probability that the...
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...
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...
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