23. There are ten urns of which each of three contains 1 white and 9 black balls, cach of otherthree contains 9 white and 1 black ball, and of the remaining four each contains 5 white and5 black balls. One of the urns is selected at random and a ball taken blindly from it turns outto be white. What is the probabililty that an urn containing 1 white and 9 black balls wasselected?

Answered: Image /qna-images/answer/c9538386-119f-4465-98b1-df0eb53f98e9.jpg

Answered: O 23. There are ten urns of which each…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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A product shipment contains 6 computer chips, of which two (2) are defective. If an inspector selects 4 chips at random for an order, without replacement, how many ways are there of picking both defective chips in this order (of 4 chips)? Order does not matter.
“ You are dealt five cards from a standard deck of 52 cards. How many of these handshave at least one queenandat least one spade. ”He breaks this into two cases. In the first case, he looks at hands which contain the queen of spadesQ♠. There is 1 way of choosing the Queen of Spades, and51C4ways of choosing the other fourcards. In the second case, he will start by choosing a non-spade queen (3 ways) and a non-queenspade (12 ways). There are 50 cards remaining, so he also throws away the Queen of Spades sothat he doesn’t overlap case 1. This gives49C3ways of choosing the last three cards. He concludesthat the answer is51C4+ (3·12·49C3). His answer is incorrect. Explain why, and give the correctanswer.
It is known that there are three boxes (I, II, III) each containing a number of black, yellow, and red balls. Box I contains 4 Black balls, 3 Yellow balls, 2 Blue balls and 3 Red balls. Box II contains 5 Black balls, 3 Yellow balls, 4 Blue balls and 2 Red balls. Box III contains 6 Black balls, 1 Yellow ball, 2 Blue balls and 3 Red balls. If a box is selected at random, then a ball is also drawn at random from the selected box, then: A) Find the probability that the ball drawn is a red ball.B) Calculate the probability that the ball comes from box I, if the chosen ball is Red!
-25-xch يتم اننا تامين بان کتوائما عن جدق فتوي عال و اتلام زرعاء Question: Two ballpoint pens are selected at random from a box that contains 3 blue pens, 2 red pens, and 3 green pens. If X is the number of Shes blue pens selected and Y is the number of red pens selected, find (a) the joint probability function Ax, y), (b) P[(X, Y) EA], where A is the region {(x, y)|x+y<1}.
A penny is tossed three times and the results heads and tails noted. The process is continued until there are 100 sets of threes. In 69 cases, heads fell first, in 49 cases, heads fell second and in 53 cases. Heads fell third. In 33 cases heads fell both first and second and in 21 cases heads fell both second and third. Show that there must have been at least 5 occasions on which heads fell three times, and that there could not have been more than 15 occasions on which tails fell three times, though there need not have been any.
Consider 3 urns. Ballot box A contains 3 white balls and 8 red balls, ballot box B contains 9 white balls and 8 red balls and ballot box C contains 10 white balls and 8 red balls. A ball is selected from ballot box 1 and placed in ballot box 2, then one is drawn from ballot box 2 and it is placed in ballot box 3, finally a ball is drawn from ballot box 3. What is the probability that the ball selected from ballot box 3 is white?
There are two urns. The first urn has 2 black balls and 1 white ball inside and there are 2 black balls and 2 white balls in the second Urn. You ask your friend to randomly choose an Urn and pick 2 balls one by one with no replacement. 1c) If one black and one white ball are selected, what is the probability that your friend selects the Urn with 3 balls inside? 1d) If we repeat this experiment from the beginning with 5 different friends. What is the probability that 2 of them get 2 black balls? 1e) On average (expected value) how many of those 5 friends will get 2 black balls?
4. In chess, each player begins the game with two Rooks (R), two Knights (N), two Bishops (B). one Queen (Q), and one King (K). These eight pieces are arranged on a player's starting row in the order R NBQKBNR), pictured here: Fischer Random is a variant of chess in which the eight starting pieces have their locations on the starting row randomized. The only conditions on this randomization are: • The King must be placed in between the two Rooks (not necessarily directly adjacent). . The two Bishops must be placed on opposite coloured squares (one light, one dark). Under these conditions, how many possible starting positions are there for a game of Fischer Random chess? Note 1: both players use the same starting configuration, so you only need to count the possible arrangements for a single player. Note 2: the traditional arrangement of pieces above is also a legal starting position for Fischer Random, so you do not need to exclude it. 1
5. A group of n people stand in a line. On the count of three, each of them simultaneously chooses to look either left or right (with equal probability): at one of their neighbors. Let X be the number of pairs of adjacent people that end up facing each other. (For example, if n = 5 and the random facings are "Left, Left, Right, Left, Right" then only the 3rd and 4th people face each other.) (a) Find the expected value E[X]. (b) Find Pr[X=0]. (c) Assuming n is even, find the maximum possible value of X, and the probability that X is equal to that value.

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