CBSE Class 12 Sample Paper for 2021 Boards

Class 12
Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

## The probabilities of A and B solving a problem independently are 1/3 πππ 1/4 respectively. If both of them try to solve the problem independently, what is the probability that the problem is solved?

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Note : This is similar to Ex 13.2, 14 of NCERT β Chapter 13 Class 12 Probability

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### Transcript

Question 15 The probabilities of A and B solving a problem independently are 1/3 πππ 1/4 respectively. If both of them try to solve the problem independently, what is the probability that the problem is solved? Given, P(A) = 1/3 & P(B) = 1/4 Probability that the problem is solved = Probability that A solves the problem or B solves the problem = P(A βͺ B) = P(A) + P(B) β P(A β© B) Since A & B are independent, P(A β© B) = P(A) . P(B) = 1/3 Γ 1/4 = 1/12 Now, P(Problem is solved) = P(A) + P(B) β P(A β© B) = 1/3 + 1/4 β 1/12 = 4/12 + 3/12 β 1/12 = 6/12 = π/π