CBSE Class 12 Sample Paper for 2024 Boards

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Question 14 - CBSE Class 12 Sample Paper for 2024 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Last updated at Dec. 13, 2024 by

A problem in Mathematics is given to three students whose chances of solving it are 1/2, 1/3, 1/4 respectively. If the events of their solving the problem are independent then the probability that the problem will be solved, is

(a) 1/4                         (b) 1/3                     (c) 1/2                    (d) 3/4

This question is similar to  Ex 13.2, 14 - Chapter 13 Class 12

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Now, Probability that the problem is solved = Probability that A solves the problem or B solves the problem or C solves the problem = P(A ∪ B ∪ C) = P(A) + P(B) + P(C) – P(A ∩ B) – P(B ∩ C) – P(C ∩ A) + P(A ∩ B ∩ C) Since A ,B & C are independent, P(A ∩ B) = P(A) . P(B) = 1/2 × 1/3 = 𝟏/𝟔 P(B ∩ C) = P(B) . P(C) = 1/3 × 1/4 = 𝟏/𝟏𝟐 P(C ∩ A) = P(C) . P(A) = 1/4 × 1/2 = 𝟏/𝟖 P(A ∩ B ∩ C) = P(A) . P(B) . P(C) = 1/2 × 1/3 × 1/4 = 𝟏/𝟐𝟒 Now, P(Problem is solved) = P(A) + P(B) + P(C) – P(A ∩ B) – P(B ∩ C) – P(C ∩ A) + P(A ∩ B ∩ C) = 1/2 + 1/3 + 1/4 − 1/6 − 1/12 − 1/8 + 1/24 = 1/2 + 1/3 + 1/4 − (1/6 " " +1/12+1/8) + 1/24 = 12/24 + 8/24 + 6/24 − (4/24 " " +2/24+3/24) + 1/24 = 26/24 − (9/24) + 1/24 = 18/24 = 𝟑/𝟒 So, the correct answer is (d)

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo