CBSE Class 12 Sample Paper for 2024 Boards

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

## (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

### Transcript

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)