# Ex 13.2, 14 - Chapter 13 Class 12 Probability

Last updated at May 29, 2018 by Teachoo

Last updated at May 29, 2018 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

Chapter 13 Class 12 Probability

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