Three houses are available in a locality. Three persons apply for the houses.

Discussion Forum : Probability I

Question -

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

Options:

A .

\frac{2}{9}

B .

\frac{2}{18}

C .

\frac{3}{8}

D .

\frac{1}{20}

Answer: Option B
:
B

For a particular house being selected Probability = $\frac{1}{3}$

Prob(all the persons apply for the same house) = $(\frac{1}{3} \times \frac{1}{3} \times \frac{1}{3}) \times 3 = \frac{1}{9}$ or $\frac{2}{18}$

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