Example 15 - Class 12
Last updated at Dec. 8, 2016 by Teachoo
Transcript
Example 15 (Method 1) A person has undertaken a construction job. The probabilities are 0.65 that there will be strike, 0.80 that the construction job will be completed on time if there is no strike, and 0.32 that the construction job will be completed on time if there is a strike. Determine the probability that the construction job will be completed on time Let A : Construction job completed on time B: There will be strike P(there will be strike) = 0. 65 P(B) = 0. 65 P(no strike) = P(B’) = 1 – P(B) = 1 – 0.65 = 0.35 So, P(B’) = 0.35 Probability that the construction job is completed on time = Probability that there will be a strike × Probability that the job is completed on time + Probability that there will not be a strike × Probability that the job is completed on time P(A) = P(B) . P(A|B) + P(B’) . P(A|B’) P(construction job is completed if no strike) = 0.80 P(A|B’) = 0.80 P(construction job is completed if no strike) = 0.32 P(A|B) = 0.32 Now, P(A) = P(B) P(A|B) + P(B’) . P(A|B’) = 0.65 × 0.32 + 0.35 × 0.80 = 0.208 + 0.28 = 0.488 Thus, required probability is 0.488 Example 15 (Method 2) A person has undertaken a construction job. The probabilities are 0.65 that there will be strike, 0.80 that the construction job will be completed on time if there is no strike, and 0.32 that the construction job will be completed on time if there is a strike. Determine the probability that the construction job will be completed on time Probability that the construction job is completed on time = Probability that there will be a strike × Probability that the job is completed on time + Probability that there will not be a strike × Probability that the job is completed on time Probability that there will not be a strike = 1 – Probability of strike = 1 – 0.65 = 0.35 Now, Probability that the construction job is completed on time = Probability that there will be a strike × Probability that the job is completed on time + Probability that there will not be a strike × Probability that the job is completed on time = 0.65 × 0.32 + 0.35 × 0.80 = 0.208 + 0.28 = 0.488 Thus, required probability is 0.488
Examples
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Example 6 Important
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Example 8
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Example 11 Important
Example 12
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Example 14
Example 15 You are here
Example 16
Example 17 Important
Example 18 Important
Example 19
Example 20 Important
Example 21 Important
Example 22
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Example 25 Important
Example 26 Important
Example 27 Important
Example 28 Important
Example 29 Important
Example 30
Example 31 Important
Example 32 Important
Example 33
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Example 35 Important
Example 36 Important
Example 37
Chapter 13 Class 12 Probability
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About the Author
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.