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) $$ \frac{1}{5} $$

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UpStudy AI · Accepted Answer

To determine the probability that a randomly selected school is a mixed school (attended by both boys and girls), let's use the principle of inclusion-exclusion.

1. **Total number of schools:** 70
2. **Schools attended by boys:** 42
3. **Schools attended by girls:** 35

Let $$ M $$ represent the number of mixed schools (attended by both boys and girls).

Using the inclusion-exclusion principle:
$$
\text{Total schools} = \text{Schools attended by boys} + \text{Schools attended by girls} - \text{Mixed schools}
$$
$$
70 = 42 + 35 - M
$$
$$
M = 42 + 35 - 70 = 7
$$

Therefore, there are **7 mixed schools** out of a total of **70 schools**.

**Probability of selecting a mixed school:**
$$
\frac{M}{\text{Total schools}} = \frac{7}{70} = \frac{1}{10}
$$

**Answer:**  
**(B) $$ \frac{1}{10} $$**
The probability of selecting a mixed school is $$ \frac{1}{10} $$.

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)
(B)
©
(D)

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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) (B) © (D)