Explain that there are (n r) different linear arrangements of n balls of which r are black and n − r are white. (The balls of the same color are undistinguishable.)
Explain that there are (n r) different linear arrangements of n balls of which r are...
a) Two balls are drawn without replacement from an urn containing 12 balls, of which 7 are white and 5 are black. Find the probability that: (i) Both balls will be white (ii) Both balls will be the same color (iii) At least one of the balls will be white b) Repeat part (a) but with the balls drawn with replacement
An urn initially contains r red balls and s black balls. A ball is selected at random but not removed and a balls of the same color as the selection are added to the urn. The process is then repeated with a balls of one color or the other added to the urn at each epoch. With each addition the population of the urn increases by a and it is helpful to imagine that the (a) What is the probability...
5. Polya's Urn +R • Begin with an urn containing W white balls and R red balls. Hence, N =W total balls. • Draw a random ball from the urn, check its color, and return it to the urn with another ball of the same color. • Now there are N + 1 balls in the urn. Draw 1 at random, check its color, and return it with another ball of the same color. . Now there are N +...
2A bin contains 10 balls, of which 3 are red, 5 are white, and 2 are black. Find the probability that all three of the selected balls have the same color. [8 pts.] 30
Two balls are chosen from an urn without replacement. 3 are black and 4 are white. Find a) the probability that both of the balls are the same color b) given that at least one of the balls is white, what is probability that the other ball is white?
Consider a set of n + m balls of which n are red and m are blue. Assume that all red balls and all blue balls are indistinguishable. How many different linear orderings are there for which no two red balls are adjacent? Please show work!
1. You own n colors, and want to use them to color 6 objects. For each object, you randomly choose one of the colors. How large does n have to be so that odds are that no two objects will have the same color (i.e., every object is colored in a different color)? 2. Consider the following game: An urn contains 20 white balls and 10 black balls. If you draw a white ball, you get $1, but if you...
B2. An urn contains k black balls and N -k white balls, with N known and k unknown. n balls are selected at random without replacement from the box. Construct a statistical model and use your statistic model to estimate k using the method-of-moments. Hint: Construct a statistical model such that the sample size is 1.
Problem(3)(20.) Suppose an urn contains 3 black balls and 4 white balls. Then, if you draw two balls without replacement, find the probability (a)both two balls are same colors. (b)two balls are different colors.
An urn contains M white and N black balls. Balls are randomly selected, one at a time, until a black one is obtained. If we assume that each ball selected is replaced before the next one is drawn, what is the probability that a) exactly x draws are needed? b) at least k draws are needed?