Consider a purple urn containing 7 red marbles and 3 blue marbles as well as a...

Consider a purple urn containing 7 red marbles and 3 blue marbles as well as a green urn containing 5 blue marbles and 4 yellow marbles. An experiment consists of drawing a marble from the purple urn, placing it in the green urn, and then drawing a marble from the green urn. Given that the marble drawn from the green urn was blue, what is the probability that the marble drawn from the purple urn was red? Give your answer to three decimal places.

Expert Solution

orchestra answered 1 year ago

Four marbles are being drawn from an urn containing 8 blue and 2 red marbles. Let...

Four marbles are being drawn from an urn containing 8 blue and 2 red marbles. Let X be the number of blue marbles drawn. What this the probability mass function for X if the marbles are drawn with replacement.

Suppose we draw 3 marbles from a jar containing 7 red and 5 blue marbles. At...

Suppose we draw 3 marbles from a jar containing 7 red and 5 blue marbles. At each stage, a ball is drawn and its color noted. Then the marble is returned to the jar along with another two marbles of the same color. Given that the ﬁrst marble is red, what is the probability that the next two are blue?

Consider an urn containing 3 red balls, 5 yellow balls, 7 blue balls, and 6 violet...

Consider an urn containing 3 red balls, 5 yellow balls, 7 blue balls, and 6 violet balls. If 4 balls are drawn at random, what is the probability of drawing one of each color? Suppose we draw 8 balls from the urn above. What is the conditional probability that 4 of them are blue with respect to the event that none of them are yellow?

An urn has marbles of red, blue, and yellow. There are seven marbles of each of...

An urn has marbles of red, blue, and yellow. There are seven marbles of each of the three colors. The experiment consists of drawing a single, random marble from the urn. Define a random variable X by X(s) = -1 if the marble has red 0, if the marble has blue +1, if the marble has yellow 54 random samples of X are taken. Approximate the probability that the mean of the sample is between 0 and 1/20.

You draw 40 times with replacement from a bag containing 7 red marbles and 3 blue...

You draw 40 times with replacement from a bag containing 7 red marbles and 3 blue marbles. A) What is the chance you will get exactly 8 blue marbles? Explain if you should use binomial formula or normal approximation. B) What is the chance that you get fewer than 20 blue marbles?Explain if you should use binomial formula or normal approximation.

Suppose you have a bag containing 2 red marbles, 3 white marbles, and 4 blue marbles....

Suppose you have a bag containing 2 red marbles, 3 white marbles, and 4 blue marbles. a) if you draw 3 marbles simultaneously, what is the probability that you get one of each color? b) If you draw 3 marbles one at a time, what Is the probability that you get one of each color?

An urn contains 5 blue marbles and 4 red marbles. You draw a certain number of...

An urn contains 5 blue marbles and 4 red marbles. You draw a certain number of marbles from the urn at random with replacement . . . (A) You win $243.00 if you draw more blue marbles than red marbles. Assuming that you want to win, which is better: drawing 20 marbles or 200 marbles? Explain your answer briefly. (B) You win $177.00 if the percentage of red marbles that you draw is less than 42%. Assuming that you want...

You randomly select 2 marbles from a mug containing 6 blue marbles, 6 red marbles, and...

You randomly select 2 marbles from a mug containing 6 blue marbles, 6 red marbles, and 3 white marbles. How many times greater is the probability of selecting 2 red marbles when you replace the first marble before selecting the second marble than when you do not replace the first marble before selecting the second marble?

(4) An urn contains 7 red marbles labeled {1,2,3,4,5,6,7} and 5 green marbles labeled {1,2,3,4,5}.Four marbles...

(4) An urn contains 7 red marbles labeled {1,2,3,4,5,6,7} and 5 green marbles labeled {1,2,3,4,5}.Four marbles are pulled out at once (i.e. with no particular order). What is the probability that ... (a) ... all four marbles are red? (b) ... more of the marbles are green than red? (c) ... both red and green marbles are present? (d) ... two of the marbles chosen are both labeled "5"?

An urn contains 4 marbles, either blue or green. The number of blue marbles is equally...

An urn contains 4 marbles, either blue or green. The number of blue marbles is equally likely to be 0, 1, 2, 3, or 4. Suppose we do 3 random draws with replacement, and the observed sequence is: blue, green, blue. What is the probability the urn contains just 1 blue marble?

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