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. $5/3$
• B. $7/12$
• C. $1/5$
• D. $2/5$

Answer 1

The correct option is C $1/5$

$n\left(H\right)=10$ {people who speak hindi}

$n\left(E\right)=8$ {People who speak English}

$n(E\cup H)=15$ (total)

$n(E\cap H)=10+8–15=3$ (Speaking both)

People who speak hindi only $=10–3=7$

Total ways of selecting $2$ people $=15C_2=105$

Favourable ways $=7C_1\times 3C_1=21$

Probability of occurrence $=\frac{21}{105}=\frac{1}{5}$