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(B) Let the total number of students in the college be $100$.Since girls constitute $60\%$ of the total students,the number of girls $= 60$ and the nu

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$\frac{3}{8}$

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(B) Let the total number of students in the college be $100$.Since girls constitute $60\%$ of the total students,the number of girls $= 60$ and the number of boys $= 100 - 60 = 40$.Number of boys studying Mathematics $= 25\% 	ext{ of } 40 = \frac{25}{100} 	imes 40 = 10$.Number of girls studying Mathematics $= 10\% 	ext{ of } 60 = \frac{10}{100} 	imes 60 = 6$.Total number of students studying Mathematics $= 10 + 6 = 16$.We need to find the probability that the student is a girl,given that the student studies Mathematics.Using the conditional probability formula,$P(	ext{Girl} | 	ext{Maths}) = \frac{	ext{Number of girls studying Maths}}{	ext{Total number of students studying Maths}}$.$P(	ext{Girl} | 	ext{Maths}) = \frac{6}{16} = \frac{3}{8}$.

In a college,$25\%$ of the boys and $10\%$ of the girls offer Mathematics. The girls constitute $60\%$ of the total number of students. If a student is selected at random and is found to be studying Mathematics,the probability that the student is a girl,is

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