6. Consider en experiment and two events A and B and their complements. The probabilityof the union of events A and B is precisely 3/4. Moreover, some other probabilities aresummarized as follows:A Ac1/8]BBc 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?

Given that: A Ac B 18 Bc 38 Union of A and B is, A∪B=34

Answered: 6. Consider en experiment and two…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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) ) =
Two people, A and B, are competing for the control of a corporation. The probabilities that these two people will win are 0.7 and 0.3, respectively. If A wins, the probability of introducing a new product is 0.8; if B wins, the corresponding probability is 0.4. a) What is the probability that a new product will be introduced? b) If a new product is introduced, what is the probability that B won the competition?
Solve the problem that involves probabilities with events that are not mutually exclusive In a class of 50 students, 21 are Democrats, 10 are business majors, and 5 of the business majors are Democrats. If one student is randomly selected from the class, find the probability of choosing a Democrat or a business major. 13 O A. 25 OB. 25 31 OC. 50 O D. 10 Next OvI 10:10 acer esc & 2# %24 3 4 1. y W * 00
Airline A is on time 80% of the time, Airline B is on time 85% of the time, and Airline C is on time 90% of the time. Airline A has twice as many flights as Airline B, and Airline B has three times as many flights as Airline C. One flight is selected at random from one of these airlines. (a) What is the probability this flight on time? (b) Given that the flight is on time, what is the probability it is from Airline A?
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.
6. A large group of people is to be checked for two common symptoms of a certain disease. It is thought that 20% of the people possess symptom A alone, 30% possess symptom B alone, 10% possess both symptoms, and the remainder have neither symptoms. For one person chosen at random from this group, find these probabilities (a) The person has neither symptom. (b) The person has at least one symptom. (c) The person has both symptoms, given that the person has symptom B.
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10 . Let A, B be independent events with P (A) = P (B) = 1/3. Find the probability that exactly one of the two will occur: Select one : a. 4/9 b. 1/9 c. 1/3 d. 2/9
If AA and BB are two mutually exclusive events with P(A)=0.35P(A)=0.35 and P(B)=0.55P(B)=0.55, find the following probabilities:a) P(A and B)= b) P(A or B)=c) P(not A)= d) P(not B)=e) P(not (A or B))= f) P(A and (not B))=

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	A	$A^{c}$
B		$\frac{1}{8}$
$B^{c}$	$\frac{3}{8}$