# 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______.

Aman Bansal
592 Points
11 years ago

Dear Shiva,

P(same house) = 1/3 * 1/3 = 1/9

Cracking IIT just got more exciting,It s not just all about getting assistance from IITians, alongside Target Achievement and Rewards play an important role. ASKIITIANS has it all for you, wherein you get assistance only from IITians for your preparation and win by answering queries in the discussion forums.

So start the brain storming…. become a leader with Elite Expert League ASKIITIANS

Thanks

Aman Bansal

upender surepally
126 Points
11 years ago

1/9

Shaurya Gupta
41 Points
11 years ago

Let 1 person select 1 house. Then the probability that 2nd and 3rd also apply for the same house is 1/3 X 1/3 as total houses are 3.

= 1/9

G Ashwin -
24 Points
11 years ago

Each person has 1/3 chance on each house.

there are 3 houses.

so,

p=1/9

36 Points
7 years ago
For particular house probability is 1/3., probability that all 3 apply for same house is 1 by (1/3 ×1/3 ×1/3 )×3
34 Points
7 years ago
Total no. Of ways a person can select a house=3C1=3Now, probability of all(selecting same house)=(1/3*1/3*1/3)*3=1/9 (ans)
Aman Gupta
13 Points
6 years ago
Let the three persons be a, b, c and the three houses be p, q, r. The event of selecting a house is an independent event. So, the probability of a, b, c selecting the house p is 1/3x1/3x1/3. Similarly, the probability of a, b, c selecting the house q is 1/3x1/3x1/3. Therefore the total probability will be 3x(1/3x1/3x1/3)=1/9
Rishi Sharma
askIITians Faculty 646 Points
4 years ago
Dear Student,
Please find below the solution to your problem.

Let 1 person select 1 house. Then the probability that 2nd and 3rd also apply for the same house is 1/3 X 1/3 as total houses are 3.
= 1/9

Thanks and Regards