Question

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. $\frac{2}{5}$

Answer 1

Answer: (C)

$\frac{1}{5}$

Answer 2

Number of persons who can speak Hindi only $= 15-8 = 7$ Number of persons who can speak both Hindi and English $= 10 + 8 - 15 = 3$ Now, probability that one person speaks Hindi only and other speaks both Hindi and English, is $\frac{^{7}C_{1}\times^{3}C_{1}}{^{15}C_{2}} =\frac{ 7\times3}{\frac{15\times14}{2}}$ $=\frac{ 7\times3\times2}{15\times14} = \frac{1}{5}$