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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______.

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______.

Grade:11

8 Answers

Aman Bansal
592 Points
10 years ago

Dear Shiva,

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

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upender surepally
126 Points
10 years ago

1/9

Shaurya Gupta
41 Points
10 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
10 years ago

Each person has 1/3 chance on each house.

there are 3 houses.

so,

p=1/9

Humanshu Parkhade
36 Points
6 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
Sawan Yadav
34 Points
5 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
4 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
2 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

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