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 persons apply for the same house is
$\frac{1}{9}$
$\frac{2}{9}$
$\frac{7}{9}$
$\frac{8}{9}$
Solution
Total number of ways $=3 \times 3 \times 3=27$
Favourable number of cases $=3$
$\therefore \quad$ Required probability $=\frac{3}{27}=\frac{1}{9}$