In class XII, suppose 5% of boys and 0.25% of girls are physically fit for a game. A fit student is selected at random from this class having same number of boys and girls. If the probability that the selected student is a girl is $\frac{m}{n}; gcd(m,n) = 1$, then $m+n$ is equal to
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 22
Let total number of boys = total number of girls = 100 (assume equal number)
Number of fit boys = 5% of 100 = 5
Number of fit girls = 0.25% of 100 = 0.25
Total number of fit students = 5 + 0.25 = 5.25
The probability that a randomly selected fit student is a girl is given by:
$\text{Probability} = \frac{\text{Number of fit girls}}{\text{Total number of fit students}} = \frac{0.25}{5.25}$
$\text{Probability} = \frac{25}{525} = \frac{1}{21}$
We are given that this fraction is $\frac{m}{n}$ where $\text{gcd}(m,n) = 1$.
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$m = 1$
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$n = 21$
Therefore:
$$m + n = 1 + 21 = 22$$