InterviewSolution
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InterviewSolution
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Two students Anil and Ashima appeared in an examination. The probability that Anil will qualify the examination is 0.05 and that Ashima will qualify the examination is 0.10. The probability that both will qualify the examination is 0.02. Find the probability that Both (a) Anil and Ashima will not qualify the examination, (b) Atlast one of them will not qualify the examination, (c) Only one of them will qualify the examination. |
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Answer» Let A: Anil qualify the examination B: Ashima qualify the examination Given: P(A) = 0.05, P(B) = 010 and P(A∩B) = 0. 02 (a) A’ : Anil will not qualify the exam and B’ : Asima will not qualify the exam. To find: P(A’∩B’) = P((A∪B)’) = 1 -P(A∩B) We have, P(A∪B) = P(A) +P(B)~ P(A∩B) = 0 05 + 0.10-0 02 P(A∪B) = 013 P(A’ ∩ B’) = 1 – P(A ∪ B) = 1 – 013 = 0.87 (b) We have P(at least one of them will not qualify the examination) = 1 – P (both of them will qualify) = 1 – P(A∩B) = 1- 0.02 =0.98 (c) Only one of them will qualify = (Anil will qualify and Ashima will not) or (Anil will not qualify and Ashima will) = (A∩B’) or (A’∩B) = (A∩B’)∪(A’∩B) Required probability = P((A∩B’)∪(A’∩B) = P(A∩B’) + P(A’∩B) = P(A)-P(A∩B) + P(B) – P(A∩B) = 0-05+ 010 – 2(0.02) = 0 15 – 0 04 = 0.11 |
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