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A bag contains 4 white and 3 black balls. Four players (A,B,C, and D) agree to take turns drawing balls from this bag(without replacement) until a white ball is drawn. If the first player (A) draws a white ball, he gets $56. If he draws a black ball, he must pay $28 into the pot. the game continues until a white ball is drawn. Find the expected value to each of the 4 players, assuming each player initially pays in...
Two bags contain a number of balls. Bag A contains 4 white and 3 black balls and bag B contains 3 whit and 5 black balls. A ball is chosen at random from bag A and placed into bag B i). Given that the first ball was black, what is the probability that a second ball drawn from bag A will be white? (1 mark) Given no knowledge of the color of the first ball, what is the probability that...
If a bag contains: 5 White Balls, 6 Red Balls, and 9 Black Balls, what is the probability of pulling out: a. A black or white ball b. A white ball c. A white ball and then a black ball without replacement? d. A white ball and then a black ball with replacement?
one bag contains 4 white balls and 3 black balls, and a second bag contains 3 white balls and 5 black balls . we first toss a fair coin .if it is head , one ball is drawn from the first bag and placed in the second bag.if it is a tail , one ball is drawn from the second bag and placed in the first bag.let the event A be that a ball is now drawn from the second...
One bag contains 4 white and 2 black balls. Another contains 3white and 5 black balls. One ball is drawn from each bag. Find theprobability that both are of same colour.
A bag contains 6 black balls,5 red balls and 4 white balls,if 3 are selected at random without replacement determine the probability that (1)all 3 are black (2)all 3 are red (3)2 are black and 1 white (4)at least 1 of each colour is selected.
Q10. A bag contains 4 white, 5 red and 6 blue balls. Consecutively 2 balls are drawn at random from the bag. The probability that all of them are red, is what? Calculate the provability for both with replacement and non-replacement.
A box contains 12 white and 8 black marbles. Two balls are drawn out randomly from the box without replacement. Let X denote the number of white balls drawn out. a. Construct the probability distribution of X. b. Find mean and variance of X using the following formula ? = E (X) = ∑ ? . ?(?) ? ?(?2) = ∑ ?2 . ?(?) ? ?2 = ???(?) = ?(?2) − (?)2
Consider 2 urns. Urn 1 has 2 White Balls and 1 Black Ball. Urn 2 has 1 White Ball and 2 Black Balls. Suppose that one ball is randomly drawn from Urn 1 and put into Urn 2. Then balls are selected one at a time without replacement from Urn 2 until a White Ball is obtained. Let Y be the number of balls drawn from Urn 2 until a white ball is drawn. Find the pdf of Y and...
2. An urn contains six white balls and four black balls. Two balls are randomly selected from the urn. Let X represent the number of black balls selected. (a) Identify the probability distribution of X. State the values of the parameters corresponding to this distribution (b) Compute P(X = 0), P(X= 1), and P(X= 2). (c) Consider a game of chance where you randomly select two balls from the urn. You then win $2 for every black ball selected and...