Example 14 - Chapter 13 Class 12 Probability
Last updated at May 29, 2018 by Teachoo
Transcript
Example 14 If A and B are two independent events, then the probability of occurrence of at least one of A and B is given by 1– P(A′) P(B′) Two events A and B are independent if P(A ∩ B) = P(A) . P(B) Probability of occurrence of at least one of A and B = Probability of occurrence of only A + Probability of occurrence of only B + Probability of occurrence of A and B = Probability of occurrence of A or B So, P(at least one of A & B) = P(A ∪ B) = P(A) + P(B) – P(A ∩ B) = P(A) + P(B) – P(A) . P(B) = P(A) + P(B) [ 1 – P(A) ] = P(A) + P(B) . P(A’) = 1 – P(A’) + P(B) . P(A’) = 1 – P(A’) [ 1 – P(B) ] = 1 – P(A’) . P(B’) ∴ P(at least one of A & B) = 1 – P(A’) P(B’) Hence Proved
Examples
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Example 6 Important
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Example 12
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Example 14 You are here
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Example 17 Important
Example 18 Important
Example 19
Example 20 Important
Example 21 Important
Example 22
Example 23
Example 24
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
Example 34
Example 35 Important
Example 36 Important
Example 37
Chapter 13 Class 12 Probability
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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.
in third last line, how P(B)P(A') changed to [1-P(B)] in the second last line ?