Each one of n persons, indexed by 1,2,..., n, has a clean hat and throws it into a box.The persons then pick hats from the box, at random. Every assignment of the hats to thepersons is equally likely. In an equivalent model, each person picks a hat, one at a time,in the order of their index, with each one of the remaining hats being equally likely to bepicked. Find the probability of the following events.Every person gets his or her own hat back.Each one of persons 1,...,m gets his or her own hat back, where 1 ≤ m

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Answered: ats from the box, at random. Every…

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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Take a Ś digit Yandom numbers o7 size So, sum each S digit Kandom numbers and consider them as Make a find its mean and valiance. a Yandom valiable. probabislity distribution and
Each of six randomly selected cola drinkers is given a glass containing cola S and one containing cola F. The glasses are identical in appearance except for a code on the bottom to identify the cola. Suppose there is actually no tendency among cola drinkers to prefer one cola to the other. Let X denote the number among the six who prefer S. 1 Calculate P(X = 3). What is the probability that at least three prefer S? ● What is the probability that at most one prefer S? 2
Suppose that you have 4 green cards and 5 yellow cards. The cards are well shuffled. You randomly draw two cards with replacement. Round your answers to four decimal places. G, = the first card drawn is green G2 = the second card drawn is green a. P(G, and G2) = b. P(At least 1 green) c. P(G2IG,) = d. Are G, and G2 independent? O They are independent event O They are dependent events
Suppose that you have 4 green cards and 5 yellow cards. The cards are well shuffled. You randomly draw two cards with replacement. Round your answers to four decimal places. G1 = the first card drawn is greenG2 = the second card drawn is green a. P(G1 and G2) = b. P(At least 1 green) = c. P(G2|G1) = d. Are G1 and G2 independent? They are independent events They are dependent events
Which one of the following statements is False (not true)? Events A and B are independent if and only if P(A and B) = P(A) x P(B). Events A and B are independent if and only if P(A) = P(A given B). O(A) x O(not A) = 1 Events A and B are independent if and only if A and B are mutually exclusive; that is disjoint. If events A and B are mutually exclusive then, P (A or B) = P(A) + P(B).
Determine whether each pair of actions results in independent or dependent events. Pick one marble out of a bag. Then, without replacing the marble, pick another marble. b a Dependent; the first marble selection will affect the second marble selection. Independent; the first marble selection will not affect the second marble selection. Dependent; the first marble selection will not affect the second marble selection. Independent; the first marble selection will affect the second marble selection. d
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Prove the theorem
A signal will fail to get through a network when the following combination of events (R n R2) U R is true. All three events (R. R2, and R) are statisticaly independent and each has a probability of 0.2. Determine the probability of no signal getting through, i.e. Determine: P ((R n Ra)U R) Select one: O a. 0.352 O b. 0.240 O c. 0.200 O d. 0.060
Which of the following pairs of events are independent? Select all that apply. 0 A. Draw a 2 of clubs from a standard deck of 52 cards, keep it, then draw a 2 of diamonds. B. Draw a 3 of spades from a standard deck of 52 cards, replace it, then draw a 5 of hearts. C. Roll a number cube. Then roll again if the first roll is a 6. OD. Roll a 2 on a number cube and spin a 3 on a spinner. E. Events A and B, where P(A) = 0.4, P(B) = 0.2, and P(A and B) = 0.8. 0 F. Events A and B, where P(A) = 0.1, P(B) = 0.5, and P(A and B) = 0.05.
Suppose that you have 5 green cards and 5 yellow cards. The cards are well shuffled. You randomly draw two cards with replacement. Round your answers to four decimal places. G1 = the first card drawn is greenG2 = the second card drawn is green a. P(G1 and G2) = b. P(At least 1 green) = c. P(G2|G1) = d. Are G1 and G2 independent? They are independent events They are dependent events
4. 60% of homeowners in Northern Virginia have a weekly lawn service. Those homes with a lawn service, 55% have a sprinkler system. For those without a lawn service, 30% have a sprinkler system. (Note: you do NOT need to simplify these answers. However, you MUST express each in terms of the events/probability notation – e.g., P(A|B) =..) a. Draw a tree diagram to model the problem b. What is the probability that a randomly selected home has a sprinkler system? c. What is the probability that a randomly selected home with a sprinkler system has a lawn service? d. What is the probability that a randomly selected home with a lawn service has a sprinkler system? e. What is the probability that a randomly selected home has a lawn service? f. What is the probability that a randomly selected home that does not have a lawn service has a sprinkler system?

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