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Question: Three houses are available in a locality. Three persons apply for the houses. Each applies for one h...

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

A

8/9

B

7/9

C

2/9

D

1/9

Answer

1/9

Explanation

Solution

For a particular house being selected. Probability = 1/3.

Probability (all the persons apply for the same house)

= (13×13×13)3=19\left( \frac { 1 } { 3 } \times \frac { 1 } { 3 } \times \frac { 1 } { 3 } \right) 3 = \frac { 1 } { 9 }