[30p] 1. The sample space S of a random experiment is given by S = {a,b, c, d, e, f, g} and!3!let A denote the event and A = {a, b, c, d}and B the event and B\A = {f.g) and%3DB'AA= {a, b)}. Pr (A') = 0.6, Pr(B) = 0.6, Pr(e) = 0.2 are known. Determine the%3Dfollowing probabilities: (a) Pr(A U B); (b) Pr(A'|B).{"\" set difference operator and "|" conditional probability}

Answered: Image /qna-images/answer/7a3cebe9-9b29-4b83-a904-5bc8ae712462.jpg

Answered: [30p] 1. The sample space S of a random…

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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Consider a random experiment that involves tossing three coins at a time. Let A = Observingexactly 2 heads and B = Observing a tail on the first coin. Findi. P(A)ii. P(B)iii. P(A U B)iv. P(A ∩ B)v. P(A|B)
Question 2 If A and B are events from a sample space such that Pr(A) = 0.6, Pr(B) = 0.3 and Pr(A U B) = 0.7, then Pr(A n B') is equal to А. О.12 В. О.18 С. 0.2 D. 0.3 Е. О.4
Given that A and B are two events where P(A) = , P(B') , P(B) = 13. and P(AUB) =7 3 Find 4 P(A|B) P(A'|B) (a) P(AOB) (b) (c) P(B'|A') (d)
5.) Suppose that a coin is tossed twice so that the sample space is S = {HH, HT, TH, TT}. Let X represent the # of tails that can come up. Create a table for its Probability Distribution Function (PDF) and draw its histogram. Test if the sum of probability is 1.
2c)
Exercise 4. Let = {a,b,c,d} and define a probability measure on 222 by P(a) = P(c) = 1/6 and P(b) = P(d) = 1/3. Define random variables X and Y by X(a) = X(b) = 2, X(c) = X(d) = −2 Y(a) = Y(d) = -1, Y(b) = Y(c) = 1. (a) List all sets in σ(Y). (b) Let Z = E(XY), determine Z(a) Z(b), Z(c) and Z(d).
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If A and B are two events and P(A) = 0.60, P(B) = 0.30 and P(A UB) = 0.80, find: %3D d) P(A' n B') e) P(A' U B') f) Р(А n В')
9. Carboxy- hemoglobin is formed when hemoglobin is exposed to carbon monoxide. Heavy smokers tend to have a high percentage of carboxyhemoglobin in their blood (Reference: A Manual of Laboratory and Diagnostic Tests by F. Fischbach). Let x be a random variable rep- resenting percentage of carboxyhemoglobin in the blood. For a person who is a regular heavy smoker, x has a distribution that is approximately normal. A random sample of n-12 blood tests given to a heavy smoker gave the following results (percentage of carboxyhemoglobin in the blood): 9.1 9.5 10.2 9.8 11.3 12.2 11.6 10.3 8.9 9.7 13.4 9.9 Where = 10.49 and s = 1.36. A long-term population mean u -10% is considered a health risk. However, a long- term population mean above 10% is considered a clinical alert that the person may be asymptomatic. We will investigate the claim: the data indicate that the population mean percentage is higher than 10% for this patient? Use a = 0.05. a. Find the test statistic. b. Find the critical…
2.3 Let A and B be two events af the same sample space. If A and B are independent and P(A) = 0.5 and P(AN H) = 0.2, then: P(B)
27. Let A and B be two given events such that P(A) = 0.6, P(B) = 0.2 and P(A/B) = %3D 0.5. Then P(A'/B') is *
17. Conditional Distributions Consider two random variables X and Y for which we know Pr(X = x) = Pr(X = x|Y = y)for all possible values of x and y. In this case we would say that X and Y are.... Pick ONE option Independent Perfectly correlated Equal to each other More than one of these choices None of these choices

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