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
  1. $\frac{2}{9}$
  2. $\frac{1}{9}$
  3. $\frac{8}{9}$
  4. $\frac{7}{9}$

Solution

For a particular house being selected Probability $=\frac{1}{3}$ Prob(all the persons apply for the same house) $=\left(\frac{1}{3} \times \frac{1}{3} \times \frac{1}{3}\right) 3=\frac{1}{9}$

Asked in: JEE Main 2005

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