Q. Out of 15 persons 10 can speak Hindi and 8 can speak English. If two persons are chosen at random, then the probability that one person speaks Hindi only and the other speaks both Hindi and English is
A) $\frac{3}{5}$
B) $\frac{7}{12}$
C) $\frac{1}{5}$
D) $\frac{2}{5}$
Explanation
(c)
Total number of persons $= 15$
and number of persons who can speak Hindi and English both
$= 10 + 8 - 15 = 3$
$\therefore$ Required probability$= \frac{\ ^{7}C_{1} \times \ ^{3}C_{1}}{\ ^{15}C_{2}} = \frac{7 \times 3}{\frac{15 \times 14}{2}} = \frac{1}{5}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.