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  • Answer please! 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

  • Option 1)

    1/9

  • Option 2)

    2/9

  • Option 3)

    7/9

  • Option 4)

    8/9

 

Answers (1)

best_answer

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

Posted by

prateek

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