32. Out of 70 schools 42 of them can be attended by boys and 35 can be attended by girls, If a pupil is selected at random from these schools, find the probability that he/she is from a mixed school. (A) \( \frac{1}{1} \) (B) \( \frac{1}{10} \) (C) \( \frac{1}{6} \) (D) \( \frac{1}{5} \)

To determine the number of mixed schools, we can use the principle of inclusion-exclusion. 1. Let \( A \) be the set of schools for boys, and \( B \) the set for girls. 2. \(|A| = 42 \) and \(|B| = 35 \). 3. The total number of schools is 70. Using the formula for inclusion-exclusion: \[ |A \cup B| = |A| + |B| - |A \cap B| \] where \(|A \cup B|\) is the total count of schools (which can be attended by either boys or girls). \[ |A \cup B| = 70 = 42 + 35 - |A \cap B| \] Solving for \(|A \cap B|\): \[ 70 = 77 - |A \cap B| \implies |A \cap B| = 7 \] Thus, there are 7 mixed schools. Now, the probability of selecting a pupil from a mixed school is given by the ratio of mixed schools to the total number of schools: \[ P(\text{mixed}) = \frac{\text{Number of mixed schools}}{\text{Total number of schools}} = \frac{7}{70} = \frac{1}{10} \] So, the answer is: (B) \( \frac{1}{10} \)