STAT-210 Home work 2. 04.3.2020 Please submit your solutions before the start of lecture on Sunday, 15t March 2020 Q. 1 Given that P(AUB) +0.7)and P(AUB) f0.9. Find P(A). Find P(B). Q. 2 Given that A and B are independent events with (i) P(A) = 2P(B) = 0.7 and P(AO B) = 0.12, find P(A B). - (ii) P(AUB)=0.8 and P(B)= 0.25 , find P(A). (iii) P(A)= 0.2 and P(B)= 0.3. Let C be the event that at least one of A or B occurs, PLA)+ P(B)-P(An %3D and let D be the event exactly one of A or B occurs. Find P(C), P(D), P(A\D), P(DA). Determine whether A and D are independent. P(AID)=PA Q. 3 Given that P(A)=0.3, P(B) = 0.5 P(AB) = 0.4. Find P(AOB), P(B A), P(AB) and P(AB). D. 4 Students in a college come from three high schools. Schools I, II and III supply espectively 15%, 40%, and 45% of the students. The failure rate of students is 5%, 3%, and P6, respectively. Find the probability that a randomly selected student chosen at random will fail. Given that a student fails, what is the probability that he or she came from school III. 5 In a certain factory, machines A, B, and C are all producing springs of the same lengt their, production, machines A, B, and C produce 3%, 1% and 2% defective spring ectively. Of the total production of springs in the factory, machine A produces 309 hine B produces 40%, and machine C produces 30%. One spring is selected at rando the total springs produced in a day. If the selected spring is defective, find t ability that it was produced by machines A, B, and C.
STAT-210 Home work 2. 04.3.2020 Please submit your solutions before the start of lecture on Sunday, 15t March 2020 Q. 1 Given that P(AUB) +0.7)and P(AUB) f0.9. Find P(A). Find P(B). Q. 2 Given that A and B are independent events with (i) P(A) = 2P(B) = 0.7 and P(AO B) = 0.12, find P(A B). - (ii) P(AUB)=0.8 and P(B)= 0.25 , find P(A). (iii) P(A)= 0.2 and P(B)= 0.3. Let C be the event that at least one of A or B occurs, PLA)+ P(B)-P(An %3D and let D be the event exactly one of A or B occurs. Find P(C), P(D), P(A\D), P(DA). Determine whether A and D are independent. P(AID)=PA Q. 3 Given that P(A)=0.3, P(B) = 0.5 P(AB) = 0.4. Find P(AOB), P(B A), P(AB) and P(AB). D. 4 Students in a college come from three high schools. Schools I, II and III supply espectively 15%, 40%, and 45% of the students. The failure rate of students is 5%, 3%, and P6, respectively. Find the probability that a randomly selected student chosen at random will fail. Given that a student fails, what is the probability that he or she came from school III. 5 In a certain factory, machines A, B, and C are all producing springs of the same lengt their, production, machines A, B, and C produce 3%, 1% and 2% defective spring ectively. Of the total production of springs in the factory, machine A produces 309 hine B produces 40%, and machine C produces 30%. One spring is selected at rando the total springs produced in a day. If the selected spring is defective, find t ability that it was produced by machines A, B, and C.
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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STAT-210 Home work 2.
04.3.2020
Please submit your solutions before the start of lecture on Sunday, 15th March 2020
Q. 1 Given that P(AUB)0.7)and P(AU B) +0.9! Find P(A). Find P(B).
Q. 2 Given that A and B are independent events with
(i) P(A) = 2P(B) = 0.7 and P(AOB) = 0.12 , find P(ĀOĒ).= - P(A)+ P(B)-P(An
(ii) P(AU B)=0.8 and P(B)=0.25 , find P(A).
(iii) P(A)= 0.2 and P(B)= 0.3. Let C be the event that at least one of A or B occurs,
%3D
and let D be the event exactly one of A or B occurs. Find P(C), P(D), P(AD),
P(DA). Determine whether A and D are independent.
P(AID)-PIA
Q. 3 Given that P(A) = 0.3, P(B) = 0.5 P(AB) = 0.4. Find P(AOB), P(BA), P(AB)
and P(AB).
Q. 4 Students in a college come from three high schools. Schools I, II and III supply
respectively 15%, 40%, and 45% of the students. The failure rate of students is 5%, 3%, and
7%, respectively.
a) Find the probability that a randomly selected student chosen at random will fail.
p) Given that a student fails, what is the probability that he or she came from school III.
5 In a certain factory, machines A, B, and C are all producing springs of the same length
their, production, machines A, B, and C produce 3%, 1% and 2% defective spring-
pectively. Of the total production of springs in the factory, machine A produces 30%-
chine B produces 40%, and machine C produces 30%. One spring is selected at randon
n the total springs produced in a day. If the selected spring is defective, find th
pability that it was produced by machines A, B, and C.
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