3. Three inspectors look at a critical component of a product. Their probabilities ofdetecting a defect are different, namely, 0.98, 0.97, and 0.96, respectively. If weassume independence, then find the probabilities of the following events:a) at least one detecting the defectb) only one finding the defectexactly two find the defectall three find the defectd)

minutes ago a) 1-((1-0.98)*(1-0.97)*(1-0.96)) = 0.9902 b) (0.98*(1-0.97)*(1-0.96)) +…

Answered: 3. Three inspectors look at a critical…

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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2.5 Question#02 Please provide detailed solution with explanation and justification asap to get a upvote for Question#02
Which of the following statements is always true? A. It is always appropriate to use the classical method to determine the probability of each outcome of an experiment. B. When computing the number of ways to randomly draw 5 marbles out of 20 marbles (without replacement) where the order does not matter, we should use the permutation rule. C. When two events A and B are mutually exclusive, then P(AnB) = P(A) + P(B). D. When two events A and B are independent, then P(A|B') = P(A), where BC represents the complement of B.
Q1: In a factory, there are three types of machines M1, M2 and M3 which produces 25%, 35% and 40% of the total bolts respectively. M1, M2 and M3 produces 5%, 4% and 2% defective bolts, respectively. A bolt is drawn at random and is found to be defective. What is the probability of that it is manufactured by: 1. machine 1? 2. machine 2? 3. machine 3?
2. Two dice are rolled. Find the probabilities of the following, as reduced fractions, and justify. Use the formula sheet if needed for help. a. P(king I card is a face card) Are the events "king" and "face card independent?
2 dice, one green and one black, are rolled once. Which of the following events are independent? 1. E= A 2 is rolled on the green die, F= A sum of 7 is rolled on both dice. 2. E= A 3 is rolled on the green die, F= A 5 is rolled on the black die. 3. E= A sum of 3 is rolled on both dice, F= A 4 is rolled on the black die. 4. E= A 2 is rolled on the green die, F= A sum of 8 is rolled on both dice.
1
4. Teddy lives life on the edge and gets dressed randomly every morning. This morning, he is randomly choosing a pair of shoes, a pair of pants, and a shirt from his closet which contains the following colors and corresponding quantities: Shoes: black (2) and brown (3) Pants: black (3) and brown (1) Shirt: white (2), brown (4) and black (6) What is the probability that Teddy randomly chooses shoes, pants and a shirt of the same color? A. 1/5 В. 2/5 С. 120 A B C D D. 3/20
An experiment consists of tossing a single die and observing the number of A, B, and C are defined as follows. A: Observe a number less than 4. B: Observe a number less than or equal to 2. C: Observe a number greater than 3. Find the probabilities associated with the following events using either the s definitions from this section. (Enter your probabilities as fractions.) (a) S (b) A|B (c) B
Q. 2 Two dice are thrown. The events A and B are taken to be Event A - "odd face on first die" Event B - "odd face on second die" Find the following probabilities: Р(А) Р(АВ) P(B) | P(B|A) Are events A and B statistically independent?
6. Consider en experiment and two events A and B and their complements. The probability of the union of events A and B is precisely 3/4. Moreover, some other probabilities are summarized as follows: A Ac 1/8] B Bc 3/8 (a) Describe the following event in terms of a union or intersection and find their prob- abilities: (i) A is observed and B is not observed. (ii) A is not observed or B is observed. (iii) B is not observed. (b) Assume that event B is observed. What is the probability that A is observed? What is the probability that A is observed assuming Bº is observed? (c) Are A and B independent?
An experiment can result in one of five equally likely simple events, E1, E2, , E5. Events A, B, and C are defined as follows. A: E1, E5 P(A) = 0.4 B: E2, E3, E4, E5 P(B) = 0.8 C: E1, E2 P(C) = 0.4 Refer to the following probabilities. P(A ∩ B) = 0.2 P(A|B) = 0.25 P(B|A) = 0.5 P(B ∪ C) = 1 P(B|C) = 0.5 P(C|B) = 0.25 Use the Addition and Multiplication Rules to find the following probabilities. (a) P(A ∪ B) P(A ∪ B) = + − = (b) P(A ∩ B) P(A ∩ B) = · P(B) = (c) P(B ∩ C) P(B ∩ C) = · P(C) = Do the results agree with those obtained by listing the simple events in each? P(A ∪ B) = P({E1, E2, E3, E4, E5}) = 1 P(A ∩ B) = P({E5}) = 0.2 P(B ∩ C) = P({E2}) = 0.2 YesNo An experiment can result in one or both of the events A and B, with the probabilities shown below. Use the probability table to answer this question. A AC B 0.37…

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