Q. I Given that P(A u B) = 0.7 and P( u B) = 0.9 . Find P(A). Find P(B).
Q. 2 Given that A and B are independent events with
(j) P(A)=2P(B)=0.7 and P(AnB)=0.12, find P(J).
(ii) P(AuB)=0.8 and P()=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, and let D be the event exactly one of A or B occurs. Find P(C) , P(D) , P(AID),P(DIA). Determine whether A and D are independent.
Q. 3 Given that P(A) = 0.3 , P(B) 0.5 P(AB) = 0.4 . Find P(A tTh B) , P(BIA) , P(ÃB) and P(ATh.
Q. 4 Students in a college come from three high schools. Schools I, II, and III supply respectively 1 5%, 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.
(b) Given that a student fails, what is the probability that he or she came from school III.
Q. 5 In a certain factory, machines A, B, and C are all producing springs of the same length. Of their, production, machines A, B, and C produce 3%, 1% and 2% defective springs, respectively. Of the total production of springs in the factory, machine A produces 30%, machine B produces 40%, and machine C produces 30%. One spring is selected at random from the total springs produced in a day. If the selected spring is defective, find the probability that it was produced by machines A, B, and C.
Q. 6 Assume 7% of people have a certain disease. A test gives correct diagnosis with a probability 0.7 i.e. if the person is sick, the test will be positive with a probability 0.7, but if the person is not sick, the test will be positive with probability 0.3. A random person from the population has tested positive for the disease. What is the probability that he is actually sick?
Q. 7 Bag I contains 4 white and 6 black balls while another Bag II contains 4 white and 3 black balls One ball is drawn at random from one of the bags and it is found to be black Find the probability that it was drawn from Bag II.
Q. 8 Suppose that 5% of all adults over 40 have diabetes. A doctor correctly diagnoses 95% of all adults over 40 with diabetes as having the disease and incorrectly diagnoses 5% of all adults over 40 without diabetes as having the disease.
(j) Find the probability that a randomly seLected adult over 40 is diagnosed as not having diabetes.
(ii) Find the probability that a randomly selected adult over 40 actually has diabetes, given that he/she is diagnosed as not having diabetes
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