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

  • Option 1)

    1/9

  • Option 2)

    2/9

  • Option 3)

    7/9

  • Option 4)

    8/9

 

Answers (1)

As we learnt in 

Probability of occurrence of an event -

Let S be the sample space then the probability of occurrence of an event E is denoted by P(E) and it is defined as 

P\left ( E \right )=\frac{n\left ( E \right )}{n\left ( S \right )}

P\left ( E \right )\leq 1

P(E)=\lim_{n\rightarrow\infty}\left(\frac{r}{n} \right )

 

- wherein

Where n repeated experiment and E occurs r times.

Reliability of a person applying to each house = \frac{1}{3}   

Reliability that they apply to same house = \frac{1}{3}\times \frac{1}{3}\times \frac{1}{3}

Therefore, Total Reliability for 3 house =3\times \frac{1}{3}\times \frac{1}{3}\times \frac{1}{3}=\frac{1}{9}

 


Option 1)

1/9

Correct

Option 2)

2/9

Incorrect

Option 3)

7/9

Incorrect

Option 4)

8/9

Incorrect

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