Three houses are available in a locality. Three persons apply for the houses. Each applies for one house…
Three houses are available in a locality. Three persons apply for the houses. Each applies for one house without consulting others. The probability that all the three apply for the same house is
$\frac{2}{9}$
$\frac{1}{9}$
$\frac{8}{9}$
$\frac{7}{9}$
Solution
For a particular house being selected
Probability $=\frac{1}{3}$
Prob(all the persons apply for the same house) $=\left(\frac{1}{3} \times \frac{1}{3} \times \frac{1}{3}\right) 3=\frac{1}{9}$