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  • Please help! If two different numbers are taken from the set {0, 1, 2, 3, ......, 10}; then the probability that their sum as well as absolute difference are both multiple of 4, is :

 If two different numbers are taken from the set {0, 1, 2, 3, ......, 10}; then the probability that their sum as well as absolute difference are both multiple of 4, is :

 

  • Option 1)

    \frac{12}{55}

  • Option 2)

    \frac{14}{45}

  • Option 3)

    \frac{7}{55}

  • Option 4)

    \frac{6}{55}

 

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.

 

Set is \left \{ 0,1,2,3--------,10 \right \}

Total ways of selecting two numbers = ^{11}{C_{2}}

=\frac{11 \times10}{2}=55

Possible pairs =\left \{ (0,4),(0,8), (2,6), (2,10),(4,8), (6,10) \right \}

Probability = \frac{6}{55}


Option 1)

\frac{12}{55}

This option is incorrect

Option 2)

\frac{14}{45}

This option is incorrect

Option 3)

\frac{7}{55}

This option is incorrect

Option 4)

\frac{6}{55}

This option is correct

Posted by

Aadil

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