Suppose a bucket contains one white and one black ball. We pick out a ball equally...

Suppose a bucket contains one white and one black ball. We pick out a ball equally likely at random and then put the ball back along with another of the same color. Then we repeat. What is the probability that the first time we pick a white ball is after the ith iteration?

Solutions

Expert Solution

here

red = black

blue = white

P(X > i) = 1/(i+1)

milcah answered 8 months ago

Next > < Previous

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...

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...

possibility tree One box contains two black balls (labeled B1 and B2) and one white ball....

possibility tree One box contains two black balls (labeled B1 and B2) and one white ball. A second box contains one black ball and two white balls (labeled W1 and W2). Suppose the following experiment is performed: One of the two boxes is chosen at random. Next a ball is randomly chosen from the box. Then a second ball is chosen at random from the same box without replacing the first ball. a. Construct the possibility tree showing all possible...

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

An urn contains two white and two black balls. A ball is drawn at random. If...

An urn contains two white and two black balls. A ball is drawn at random. If it is white, it is not replaced into the urn, otherwise it is replaced with another ball of the same color. The process is repeated. Find the probability that the third ball drawn is black.

7. A box contains 12 white marbles and 5 black marbles. Suppose we randomly draw a...

7. A box contains 12 white marbles and 5 black marbles. Suppose we randomly draw a marble from the box, replace it, and then randomly draw another marble from the box. (This means that we might observe the same marble twice). What is the probability that both the marbles are white? Write your answer as a decimal accurate to three decimal places. 8. Suppose that 7.3 % of the items produced by a factory are defective. If 5 items are...

a box contains two red balls , one white ball and one blue ball. A sample...

a box contains two red balls , one white ball and one blue ball. A sample of two balls was drawn randomly, respectively (without return), If the variable X express the number of white balls and the variable Y express the number of blue balls in the sample, find : A- Fxy(0,1) B- Coefficient of correlation between the two variables and then commented on it

Urn problem One jar contains 8 white marbles and 12 black marbles. We offer you the...

Urn problem One jar contains 8 white marbles and 12 black marbles. We offer you the following three games. For each game, identify the probability law(distribution) that will follow the number of points you will earn, the expected value and its Standard deviation. A) You draw ten marbles and earn one point for each white ball drawn. (with replacement) B)You draw ten marbles and earn one point for each white ball drawn. (Without replacement) C) You draw marbles (with replacement)...

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...

An urn contains 7 black balls, 4 red balls, 3 white balls and 1 blue ball,...

An urn contains 7 black balls, 4 red balls, 3 white balls and 1 blue ball, and a player is to draw one ball. If it is black, he wins $1, if it is red, he wins $2, if it is white he wins $3 and if it is blue, he pay $25. a. Set up the empirical probability distribution for the random variable X, the payoff of the game. Game Payoff (X) Probability [P(X) $1 $2 $3 $4 b....

Subjects