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14.Probability
hard
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
A
$\frac{1}{6}$
B
$\frac{3}{8}$
C
$\frac{5}{8}$
D
$\frac{5}{6}$
Solution
(b) Let $100$ students studying in which $60\%$ girls and $40\%$ boys.
Boys $= 40$, Girls $= 60$
$25\%$ of boys offer Maths $= \frac{{25}}{{100}} \times 40 = 10$ Boys
$10\%$ of girls offer Maths $=\frac{{10}}{{100}} \times 60 = 6$ Girls
It means, $16$ students offer Maths.
$\therefore $Required probability $ = \frac{6}{{16}} = \frac{3}{8}$.
Standard 11
Mathematics
