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!
(b) At time n = 0, an urn contains 2m balls, of which m are red and m are blue. At each time n = 1, ..., 2m, a single ball is randomly selected and taken away with no replacement. Hence, at time n, the urn has 2m – n balls. Let Rn denotes the number of red balls remaining in the urn at time n. For n= 0,..., 2m – 1, let B Rn Pn = 2m - in...
Consider an urn containing 6 red balls and 3 blue balls from which 3 balls are selected without replacement. What is the probability of selecting a red ball, if you select exactly one blue ball?
19 red 11 Blue 20 Yellow given the number of red, blue, and yellow balls in a box. In how many ways can one yellow and two red balls be taken from the box, with replacement? please with the formula
You have 6 red balls, three of which are identical and the other three are distinct and different from the previous three, 4 distinct yellow balls, 5 identical blue balls. You want to select 7 balls to make a gift bag. How many different options per gift bag do you have?
1. Consider an urn with 4 blue balls, 6 red balls, and 3 yellow balls. Suppose we draw 4 balls at random. (a) How many elements are in the sample space? (b) What is the probaiblity that we draw 4 red balls? (c) What is the probability that we draw 2 red balls and 2 blue balls? (d) What is the probability that we draw either 3 blue and 1 yellow ball or 1 blue and 3 yellow balls? 2....
Urn R contains n red balls and urn B contains n blue balls. At each stage a ball is selected at random from each urn and they are swapped. Show that the expected number of red balls in urn R after stage k is: **(1+(1-3)
Suppose that an urn contains 10 red balls and 4 white balls. Supposed 3 balls are drawn one by one from the urn. What is the probability of getting one red ball and two white balls? Show all work! a) Assume the balls are drawn with replacement. b) Assume the balls are drawn without replacement.
Suppose that two balls are drawn in succession from a bag containing 5 red balls, 4 green balls, and 3 blue balls with the assumption that the first ball is replaced befire a second one is drawn. How many ways will be drawing both red or both blue ?
Consider an urn with 10 blue balls, 5 green balls and 5 red balls. One ball is randomly drawn from the urn, and is associated with a score of X as follows: if a blue ball is drawn X = 2, if a green ball is drawn X = 1 and if a red ball is drawn (a) Compute E(X) and Var(X) (b) A game is played in which a player pays S3 and gets winnings of S2* For example,...
8. In a lottery, 6 balls are drawn randomly from a set of 49 balls numbered 1, 2, . . . , 49. You choose 6 numbers on your ticket, and you win if you have the same 6 numbers as the numbers of the balls that are drawn. It does not matter if your numbers are in the same order as the order the balls are drawn (order does NOT matter). We consider two different lottery rules in the...