Different illnesses can produce identical symptoms. Suppose a particular set of symptoms, which we will denote as event H,occurs only when any one of three illnesses-A, B, or C-occurs. (For the sake of simplicity, we will assume that illnesses A, B, andC are mutually exclusive.) Studies show the following probabilities of getting the three illnesses.P(A) = 0.09P(B) = 0.005P(C) = 0.07The probabilities of developing the symptoms H, given a specific illness, are as follows.P(HIA) 0.65P(HIB) = 0.95P(HIC) 0.85Assuming that an ill person shows the symptoms H, what is the probability that the person has illness A? (Round your answer tofour decimal places.)

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Answered: Different illnesses can produce…

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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Example 8.28 Two computers A and B are to be marketed. A salesman who is assigned a job of finding customers for them has 60 per cent and 40 per cent chances respectively of succeeding in case of computers A and B. The computers can be sold independently. Given that he was able to sell at least one computer, what is the probability that the computer A has been sold?
If A denotes some event, what does A denote? If P(A) = 0.996, what is the value of P(Ā)? ..... What does Ā denote? O A. Event Ā denotes the complement of event A, meaning that Ā and A share some but not all outcomes. O B. Event Ā is always unusual. °C. Event Ā denotes the complement of event A, meaning that Ā consists of all outcomes in which event A does not occur. O D. Events A and Ā share all outcomes. If P(A) = 0.996, what is the value of P(Ā)? P(A) = (Type an integer or a decimal. Do not round.)
(i) If volume is high this week, then next week it will be high with a probability of 0.9 and low with a probability of 0.1.(ii) If volume is low this week then it will be high next week with a probability of 0.5.Assume that state 1 is high volume and that state 2 is low volume. 1. If the volume this week is high, what is the probability that the volume will be high two weeks from now? 2. What is the probability that volume will be high for three consecutive weeks?
If an experiment is conducted, one and only one of three mutually exclusive events S1, S2, and S3 can occur, with these probabilities: P(S1)=0.2, P(S2)=0.5, P(S3)=0.3. The probabilities of a fourth event A occurring, given that event S1, S2, or S3 occurs, are P(A|S1)=0.02, P(A|S2)=0.01, P(A|S3)=0.03. Find P(S3|A)?
. Initial diagnosis of a patient’s illness was potentially flu (F), cold (C), or hay fever (H), with probabilities 0.1, 0.2, and 0.7 respectively. A lab test was then taken from the patient. Past tests on similar patients show the following conditional probabilities on the test result being positive (+), neutral (0), or negative (-):•P(+|F) = 0.7P(0|F) = 0.2P(-|F) = 0.1•P(+|C) = 0.1P(0|C) = 0.8P(-|C) = 0.1•P(+|H) = 0.1P(0|H) = 0.2P(-|H) = 0.7•Use the Bayes Theorem to estimate the respective probabilities of F, C, and H given that a +, 0, or – test result has been observed.
If two events are statistically independent, then the probability that they both occur is: a. 0 b. 0.5 c. 1.0 d. the product of their marginal probabilities e. cannot be determined with the information given.
Suppose we have events A, B, and C with probabilities: P ( A ) = 0.4 , P ( B ) = 0.2 , P ( C ) = 0.3. We also know that: A and B are independent, A and C are mutually exclusive, and P ( B ∩ C ) = 0.15 Compute each of the following. Write your answers as decimals. P ( A ∩ B ) = P ( A ∪ B ) = P ( B ∪ C ′ ) =
Suppose the probability of a typical tax return having an illegitimate deduction is 0.2. An IRS auditor examines 6 independent tax returns. What is the probability the auditor will see (a) exactly 2 illegitimate tax deductions (b) less than 2 illegitimate tax deductions Problem 3 (10 points). Suppose the probabilities
1. You and your 4 other friends play 5 ranked games in Mobile Legends every day for the past few months. As you play with them, you recorded the number of wins you have per day. The table below shows the number of wins you have per day and their corresponding probabilities. 1 2 3 4 5 P(X=x) 0.082 0.246 0.393 0.262 0.002 0.015 If you are planning to play 5 ranked games with them today, how many wins will you expect? a. 3 wins b. 1 win c. None of the choices d. 4 wins e. 2 wins
An experiment consists of 5 elementary outcomes, with the following probabilities: e | Pr(e) e1 | 0.1 e2 | 0.1e3 | 0.2e4 | 0.3e5 | 0.3 If E = {e1,e2,e3} and F = {e2,e3,e4}, then Pr(E and F) isa. .50 b. .70 c. .67 d. .30
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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