Three Integers are  randomly chosen without replacement from to first 20 postive integer. Find the problality that this 3 intgless from an A.P

  • Option 1)

    \frac{5}{38}

  • Option 2)

    \frac{1}{19}

  • Option 3)

    \frac{3}{38}

  • Option 4)

    \frac{2}{19}

 

Answers (1)
V Vakul

 

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.

 

  Total Sum A.P series is 

2+4+---18

=\frac{9}{2}\left [ 2+18 \right ]=\frac{9}{2}\times 20

9\times 10=90

and  3 number are chosen from

20 number is  20_{C_{3}}

\therefore Required Probability =\therefore \frac{90}{20_{C_{3}}}=\frac{90}{1410}

=\frac{9}{141}=\frac{3}{38}


Option 1)

\frac{5}{38}

Option is incorrect

Option 2)

\frac{1}{19}

Option is incorrect

Option 3)

\frac{3}{38}

Option is correct

Option 4)

\frac{2}{19}

Option is incorrect

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