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Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class12  >>  Probability
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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 :

$\begin {array} {1 1} (A)\;\large\frac{8}{9} & \quad (B)\;\large\frac{7}{9} \\ (C)\;\large\frac{2}{9} & \quad (D)\;\large\frac{1}{9} \end {array}$


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For a particular house being selected, probability = $ \large\frac{1}{3}$
Probability all the persons apply for the same house = $ \bigg( \large\frac{1}{3} \times \large\frac{1}{3} \times \large\frac{1}{3} \bigg) 3$
$ = \large\frac{1}{27} \times 3$
$ = \large\frac{1}{9}$
Ans : (D)
answered Jan 3, 2014 by thanvigandhi_1

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