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) ) =
Urn A contains x red marbles and y white marbles, and urn B contains z red marbles and v white marbles. (i) If an urn is selected at random and a marble drawn, what is the probability that the marble is red? (ii) If a marble is drawn from urn A and put into urn B and then a marble is drawn from urn B, what is the probability that the second marble is red?
2. (Finite Stochastic Processes). If a baseball team wins a game, they have a 39% chance of winning the next game due to getting overconfident (draws/ties should not occur in baseball). If they lose the previous came, there is a 67.5% chance they will win the next game. Assume that for the first game there is a 50% chance of winning. What is the probability the team wins the fourth game? Please give a complete, fully typed, solution to the problem. Please do not submit photos of hand-written notes instead of properly typed math text! (this may lead to going back “on" the screening, if you are currently "off" the screening).
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
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2. (Finite Stochastic Processes). If a baseball team wins a game, they have a 39.5% chance of winning the next game due to getting overconfident (draws/ties should not occur in baseball). If they lose the previous came, there is a 67% chance they will win the next game. Assume that for the first game there is a 50% chance of winning. What is the probability the team wins the fourth game? Please give a complete, fully typed, solution to the problem. Please do not submit photos of hand-written notes instead of properly typed math text! (this may lead to going back "on" the screening, if you are currently "off" the screening).
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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