Question

In: Statistics and Probability

Suppose that we have two bags each containing black and white balls. One bag contains two...

Suppose that we have two bags each containing black and white balls. One bag contains two times as many white balls as black balls. The other bag contains two times as many black balls as white. Suppose we choose one of these bags at random. For this bag we select five balls at random, replacing each ball after it has been selected. The result is that we find all balls are white balls. What is the probability that we were using the bag with mainly black balls?

Solutions

Expert Solution


Related Solutions

19. We have two boxes; there are m white balls and one black ball in the...
19. We have two boxes; there are m white balls and one black ball in the first box, and k white balls and one black ball in the second box. We randomly choose a box (each choice has the same probability) and then draw two balls simultaneously from the chosen box. Let X denote the number of black balls drawn, and Y denote the number of the box that was chosen. Find the correlation coefficient of variables X and Y...
A box contains three white balls, two black balls, and one red ball. Three balls are...
A box contains three white balls, two black balls, and one red ball. Three balls are drawn at random without replacement. Let Y1 be the number of white balls drawn, and Y2 the number of black balls drawn. Find the distribution of Z = Y1 × Y2
A bag contains two orange and six black balls. You take two balls from the bag,...
A bag contains two orange and six black balls. You take two balls from the bag, one by one, with replacement. How many orange balls do you expect to get?
Suppose there are three balls in a bag. One ball is black and two others are...
Suppose there are three balls in a bag. One ball is black and two others are white. Three people, A, B and C, will pick a ball in this order. Instead of deciding the winner by the first black ball, the person who picks the black ball for the second time will be the winner. For example, if A picks the black ball for his first pick, A is not the winner. He just returns it to the bag. And...
Suppose that Phil and Jen each have a bag containing 10 distinguishable objects. The two bags...
Suppose that Phil and Jen each have a bag containing 10 distinguishable objects. The two bags have the same content. Phil and Jen randomly choose 3 objects each from their bags. Consider the following random variables: X − the number of objects chosen by both Phil and Jen Y − the number of objects not chosen by either Phil or Jen Z − the number of objects chosen by exactly one of Phil and Jen Compute E(X), E(Y ) and...
Suppose that Phil and Jen each have a bag containing 10 distinguishable objects. The two bags...
Suppose that Phil and Jen each have a bag containing 10 distinguishable objects. The two bags have the same content. Phil and Jen randomly choose 3 objects each from their bags. Consider the following random variables: X − the number of objects chosen by both Phil and Jen Y − the number of objects not chosen by either Phil or Jen Z − the number of objects chosen by exactly one of Phil and Jen Compute E(X), E(Y ) and...
We have a bag that contains n red balls and n blue balls. At each of...
We have a bag that contains n red balls and n blue balls. At each of 2n rounds we remove one of the balls from the bag randomly, and place it in one of available n bins. At each round, each one of the balls that remain in the bag is equally likely to be picked, as is each of the bins, independent of the results of previous rounds. Let Nk be the number of balls in the k-th bin...
Suppose that there is a white urn containing two white balls and three red balls and...
Suppose that there is a white urn containing two white balls and three red balls and there is a red urn containing two white balls and four red balls. An experiment consists of selecting at random a ball from the white urn and then​ (without replacing the first​ ball) selecting at random a ball from the urn having the color of the first ball. Find the probability that the second ball is red.
Urn A contains four white balls and three black balls. Urn B contains six white balls...
Urn A contains four white balls and three black balls. Urn B contains six white balls and seven black balls. A ball is drawn from Urn A and then transferred to Urn B. A ball is then drawn from Urn B. What is the probability that the transferred ball was white given that the second ball drawn was white? (Round your answer to three decimal places.) I can't seem to figure this out! Please help! Thank you!
Following are three boxes containing balls. Box #1 contains 2 black balls and 1 white ball....
Following are three boxes containing balls. Box #1 contains 2 black balls and 1 white ball. Box #2 contains 2 black balls and 2 white balls. Box #3 contains 1 black ball and 2 white ball. Draw a ball from Box 1 and place it in Box 2. Then draw a ball from Box 2 and place it in Box 3. Finally draw a ball from Box 3 . What is the possibility that the last ball drawn, from Box...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT