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8. (1) Given that three events A, B and Care such that P(A) - P(C), P(A n) P(An C) P(C\B) = 2/7 and P(B U C) - 4/5 find %3D (a) P(A), (b) Р(В). HIN

8. (1) Given that three events A, B and Care such that P(A) - P(C), P(A n) P(An C) P(C\B) = 2/7 and P(B U C) - 4/5 find %3D (a) P(A), (b) Р(В). HIN

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Answer detailly 8(i)

8. (i) Given that three events A, B and C are such that P(A) = P(C), P(ANC). P(AN C) P(CB) = 2/7 and P(BU C) = 4/5 find (a) P(A), (b) P(B). (ii) The desks in a certain classroom are produced by three different carpenters A, B and C. A produces 30 %, B produces 45 % and the rest are produced by C. It is known that 3 % of the desks produced by 4, 6 % of those produced by B and 4 % of those produced by C, are defective. A desk is selected from this classroom at random. (c) Draw a tree diagram showing all the possible outcomes (d) Find the probability that the desk is defective. Given that the desk is defective, find the probability that it was produced by C. (e) HIN
Transcribed Image Text:8. (i) Given that three events A, B and C are such that P(A) = P(C), P(ANC). P(AN C) P(CB) = 2/7 and P(BU C) = 4/5 find (a) P(A), (b) P(B). (ii) The desks in a certain classroom are produced by three different carpenters A, B and C. A produces 30 %, B produces 45 % and the rest are produced by C. It is known that 3 % of the desks produced by 4, 6 % of those produced by B and 4 % of those produced by C, are defective. A desk is selected from this classroom at random. (c) Draw a tree diagram showing all the possible outcomes (d) Find the probability that the desk is defective. Given that the desk is defective, find the probability that it was produced by C. (e) HIN
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