Consider the sample space S = {Silicon, Germanium, Nitrogen, Gallium, Carbon,Indium} and the eventsA = {Silicon, Germanium, Indium}B = {Germanium, Nitrogen, Gallium}C = {Carbon}List the elements of the sets corresponding to the following events:(a) Ā;(b) AU C;(c) (AUB) N (AUC);

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Answered: Consider the sample space S = {Silicon,…

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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If two events A and B area such that P(A)=0.3, P(B) = 0.4 and P(AB)=0.5 then P(B|AUB))= (a) 1/ 1225 (c) 2 (b) 1 (d) 1314
b)
3. Five people, including you and a friend, line up in a random order. Let X count the number of people in the line standing in between you and your friend. (a) Find the pmf px(x) by constructing a neat, organized table of values. Express your answers as fractions in lowest terms. (Note that a waiting line is ordered. Permutations are needed here.) (b) Find Var (X). Express your answer as a decimal.
Question 5 (a) Two independent events, A and B, are such that, P(A) = 0.7 and P(B) = 0.4, calculate: (i) P(AN B) (ii) P(A U B) (b) A team of 5 people is to be formed from 4 men and 6 women. Find the number of possible teams if there are: (i) No restrictions. (ii) More women than men on the team.
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Assume A and B are independent events with P(A) = 0.42 and P(B) = 0.65. Find (a) P(A n B), (b) P(AUB), (c) P (A'n B'), (d) P (A'n B), and (e) P(ANB'). ... (a) P(An B) = (Type an integer or a decimal.) (b) P(A U B) = (Type an integer or a decimal.) (c) P (A'n B') = (Type an integer or a decimal.) (d) P (A' n B) = (Type an integer or a decimal.) (e) P (An B') = (Type an integer or a decimal.)
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3. Oil exploration : Let D and E be two events in a sample space. It is given that P (D) = 0.4, P (E) = 0.5 and P (DUE) = 0.8. (a) Are the events D and E disjoint? Are the events D and E independent? Then to oil exploration. We imagine two oil fields. The event B = "oil discovery on field 1", while the complementary event B' = "no oil on field 1". Similarly, the event C = "oil discovery on field 2", while C' = "no oil on field 2". We are given that P (B n C) = 0.06, P (B' n C) = 0.12, P (B n C') = 0.11 and P (B' n C') = 0.71. (b) Find the probability of oil on field 1. Assume that oil has been found on field 2. What is now the probability of oil on field 1? Assume that it has been proven that field 2 does not contain oil. What is now the probability of oil on field 1? Are events B and C independent?
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Consider the sample space S = {Silicon, Germanium, Nitrogen, Gallium, Carbon, Indium} and the events A = {Silicon, Germanium, Indium} B = {Germanium, Nitrogen, Gallium} C = {Carbon} List the elements of the sets corresponding to the following events: (a) Ā; (b) AU C; (c) (AUB) N (AUC);