3.97 Guannan draws three balls at random and without replacement from a bag that contains five...
1. We draw randomly without replacement 3 balls from an urn that contains 3 red and 5 white balls. Denote by X the number of red balls drawn. Find the probability distribution of X, its expected value, and its standard deviation.
an urn contains n red and n blue balls. Balls are drawn at random (without replacement) in stages until one color is depleted. The number of draws until this event happens is called waiting time. what is the distribution of this waiting time?
Suppose three balls are drawn (with replacement) from a bag that contains 2 white balls and 3 orange balls. The number of orange balls is counted. Complete parts (a) and (b) below. (a) Determine the histogram for the number of orange balls in the sample. Choose the correct histogram below. A OB OC. A P() 1- AP(x) 1- AP(x) 1- OD. AP(x) 1- 0.5- 0.5- 0.5- 0.5- X 0 0 1 2 3 0 1 2 3 0 1 2...
Two balls are drawn in succession without replacement from a bag containing 2 red balls, 1 green balls and 3 green balls. Let X and Y denote the number of red and green balls respectively. Find a) f(x,y) the expression for the joint p.d.f of X and Y [5 Marks] b) f(x) the expression for the marginal pdf of X [5 Marks] c) f(y) the expression for the marginal pdf of Y [5 Marks] d) f(y/x), the expression for the...
Two balls are drawn, without replacement, from a bag containing 13 red balls numbered 1−13 and 4 white balls numbered 14−17. (Enter your probabilities as fractions.) (a) What is the probability that the second ball is red, given that the first ball is white? (b) What is the probability that both balls are even-numbered? (c) What is the probability that the first ball is red and even-numbered and the second ball is even-numbered?
Michael has a box of colored balls. It contains two red balls, two green balls, two yellow balls, and five blue balls. Michael draws a ball at random from the box Let R denote the event that the ball he draws is red, and let B denote the event that the ball he draws is blue. What is Pr(R|B)? What is Pr(R|B′)? Enter your answers as whole numbers or fractions in lowest terms. A bag contains four 1-dollar bills, three...
A bag contains 4 white, 5 red and 6 blue balls. Three balls are randomly drawn, without replacement, from the bag. What is the probability that the first two balls are red and the last one is blue?
A box contains 3 red and 4 green marbles. Five marbles are drawn without replacement. Let X denote the number of red marbles obtained. a) Construct the probability distribution of X. b) What is the expected number of red marbles?
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...
Four balls are selected at random without replacement from an urn containing three white balls and five blue balls. Find the probability that two or three of the balls are white.