1. Tardigrade
  2. Question
  3. Mathematics
  4. 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:

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. 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:

AIEEEAIEEE 2005Probability - Part 2

Solution:

Person 1 has three options to apply.
Similarly, person 2 has three options to apply and person 3 has three options to apply.
Total cases $= 3^3$
Now, favourable cases = 3 (An either all has applied for house 1 or 2 or 3}
So probability $= \frac{3}{3^{3}} = \frac{1}{9}.$