# Example 14 - Chapter 13 Class 12 Probability

Last updated at Feb. 15, 2020 by Teachoo

Last updated at Feb. 15, 2020 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 ∩ 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 Given, A & B are independent So, P(A ∩ B) = P(A) . P(B)

Examples

Example 1

Example 2

Example 3

Example 4

Example 5 Important

Example 6

Example 7 Important

Example 8

Example 9 Important

Example 10

Example 11 Important

Example 12 Important

Example 13 Important

Example 14 Important You are here

Example 15 Important

Example 16

Example 17 Important

Example 18 Important

Example 19 Important

Example 20 Important

Example 21 Important

Example 22

Example 23

Example 24 Important

Example 25 Important

Example 26 Important

Example 27 Deleted for CBSE Board 2021 Exams only

Example 28 Important Deleted for CBSE Board 2021 Exams only

Example 29 Important Deleted for CBSE Board 2021 Exams only

Example 30 Important Deleted for CBSE Board 2021 Exams only

Example 31 Important Deleted for CBSE Board 2021 Exams only

Example 32 Important Deleted for CBSE Board 2021 Exams only

Example 33 Important

Example 34 Important Deleted for CBSE Board 2021 Exams only

Example 35 Important

Example 36 Important

Example 37 Important

Chapter 13 Class 12 Probability

Serial order wise

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.