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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 three apply for the same house is

Options

  1. A1 4
  2. B8 9
  3. C7 9
  4. D1 9

Correct answer

D. 1 9

Step-by-step solution

Each of the three persons can apply for any of the three houses. Since each person has 3 choices, the total number of ways for three persons to apply for the houses is 3 3 3 = 3^3 = 27 . For all three persons to apply for the same house, they must all choose house 1, or all choose house 2, or all choose house 3. There are 3 such favorable outcomes. The probability is the ratio of the number of favorable outcomes to the total number of outcomes: P = 3 27 = 1 9 Answer: 1 9

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