# Ex 13.2, 14

Last updated at March 11, 2017 by Teachoo

Last updated at March 11, 2017 by Teachoo

Transcript

Ex 13.2, 14 Probability of solving specific problem independently by A and B are 12 and 13 respectively. If both try to solve the problem independently, find the Probability that (i) the problem is solved. Two events A & B are independent if P(A ∩ B) = P(A) . P(B) Given, P(A) = 12 & P(B) = 13 Probability that the problem is solved = Probability that A solves the problem or B solves the Problem = P(A ∪ B) = P(A) + P(B) – P(A ∩ B) Since A & B are independent, P(A ∩ B) = P(A) . P(B) = 12 × 13 = 16 Now, P(Problem is solved) = P(A) + P(B) – P(A ∩ B) = 12 + 13 – 16 = 36 + 26 – 16 = 46 = 𝟐𝟑 Ex 13.2, 14 Probability of solving specific problem independently by A and B are 12 and 13 respectively. If both try to solve the problem independently, find the Probability that (ii) exactly one of them solves the problem. Two events A & B are independent if P(A ∩ B) = P(A) . P(B) Given, P(A) = 12 & P(B) = 13 Probability that exactly one of them solves the problem = Probability that only A solves + Probability that only B solves P(exactly one of them solves) = P(A alone) + P(B alone) = P(A ∩ B’) + P(B ∩ A’) = (P(A) – P(A ∩ B)) + (P(B) – P(B ∩ A)) = P(A) + P(B) – 2P(A ∩ B) = 12 + 13 – 2 × 16 = 12 + 13 – 13 = 12

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Important Question for exams Class 12

- Chapter 1 Class 12 Relation and Functions
- Chapter 2 Class 12 Inverse Trigonometric Functions
- Chapter 3 Class 12 Matrices
- Chapter 4 Class 12 Determinants
- Chapter 5 Class 12 Continuity and Differentiability
- Chapter 6 Class 12 Application of Derivatives
- Chapter 7 Class 12 Integrals
- Chapter 8 Class 12 Application of Integrals
- Chapter 9 Class 12 Differential Equations
- Chapter 10 Class 12 Vector Algebra
- Chapter 11 Class 12 Three Dimensional Geometry
- Chapter 12 Class 12 Linear Programming
- Chapter 13 Class 12 Probability

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.