A certain system can experience three different types of defects. Let A, (i = 1,2,3) denote the event that the system has a defect oftype i. Suppose that the following probabilities are true.P(A,) = 0.14P(A, UA,) = 0.17P(A, U Az) = 0.15P(A,) = 0.11 P(A,) = 0.08P(A, UA,) = 0.18P(A, N Az n Ag) = 0.02(a) What is the probability that the system does not have a type 1 defect?(b) What is the probability that the system has both type 1 and type 2 defects?(c) What is the probability that the system has both type 1 and type 2 defects but not a type 3 defect?(d) What is the probability that the system has at most two of these defects?

Answered: A certain system can experience three…

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 A and B are two mutually exclusive events with P(A)= 0.5 and P(B)=0.4, find the following probabilities: a) P(A \textrm{ and } B) = 0.5 b) P(A \textrm{ or } B) = c) P( \textrm{not }A ) = d) P( \textrm{not }B ) = 0.4 e) P( \textrm{not }(A \textrm{ or } B)) = 0.4 f) P( A \textrm{ and } (\textrm{not }B) ) =
An experiment can result in one of five equally likely simple events, E₁, E₂, A: E₂, E4 2' P(A) = = 0.4 B: E₁, E3, E4, E5 P(B) = 0.8 C: E₂, E3 Refer to the following probabilities. P(A n B) = 0.2 P(AIB) = 0.25 P(BIA) P(BU C) = 1 P(BIC) 0.5 P(CIB) 0.25 Use the Addition and Multiplication Rules to find the following probabilities. (a) P(AUB) (b) P(An B) = 0.5 P(A U B) = ---Select--- + ---Select--- ✓ P(A n B) = ---Select--- (c) P(B n C) Yes P(B n C) = ---Select--- No P(C) = 0.4 . P(B) = = P(C) = = ---Select--- V = Do the results agree with those obtained by listing the simple events in each? P(A U B) = P({E₁, E₂, E3, E4, E5}) = 1 P(A n B) = P({E₁}) = 0.2 P(B n C) = P({E3}) = 0.2 .., E5. Events A, B, and C are defined as follows.
How can I answer the letters b, c, and d of question 26?
One student is selected at random from a group of 200 known to consist of 140 full-time (80 female and 60 male) student and 60 part-time (40 female and 20 male) students. Event A is "the student selected is full-time" and event C is "the student selected is female". (a) Are events A and C independent? (b) Find the probability of one student selected is full-time, that should be female.
One of two biased coins A and B is selected and flipped 2 times. Let A be the event that coin A is selected and B be the event that coin B is selected, with probabilities p(A) = 0.1 and p(B) = 0.9. When coin A is flipped, the probability of heads is 0.4. When coin B is flipped, the probability of heads is 0.8. Y, and Z in Let HH be the event that the selected coin comes up heads 2 times. Complete the values Bayes' Theorem to determine the probability coin B was chosen if both come up heads. X Ex: 0.123 · 0.9 p(B|HH) Ex: 0.123 · 0.9 + Ex: 0.123 · 0.1 Y
Suppose that 55% of all adults regularly consume coffee, 45% regularly consume carbonated soda, and 70% regularly consume at least one of these two products. (a) What is the probability that a randomly selected adult regularly consumes both coffee and soda? (b) What is the probability that a randomly selected adult doesn't regularly consume at least one of these two products?
Suppose that 50% of all adults regularly consume coffee, 40% regularly consume carbonated soda, and 65% regularly consume at least one of these two products. (a) What is the probability that a randomly selected adult regularly consumes both coffee and soda? (b) What is the probability that a randomly selected adult doesn't regularly consume at least one of these two products?
A congressional committee is composed of 10 members: 6 Republicans and 4 Democrats. On any given vote, members vote independently. Whereas Republicans always vote their party line, Democrats vote their party line with probability .8, and vote Republican with probability .2. On a rainy day only 3 committee members (selected w/o replacement) were present. Let X = number of Democrats present Y = Number who voted Democratic that day Display the table of joint probabilities fX,Y(i,j) for 0 ≤ j ≤ i, for i=0,1,2,3. We can say that p(i,j)=P[x=i, Y=j].

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