A pair of dice is rolled again and again till a total of 5 or 7 is obtained. The chance(probability) that a total of 5 comes before a total of 7 is?

  • Option 1)

    \frac{2}{5}

  • Option 2)

    \frac{3}{7}

  • Option 3)

    \frac{3}{13}

  • Option 4)

    None of these

 

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.

 

 P(A)=\frac{4}{36}, B(B)=\frac{6}{36}, P(C)=\frac{26}{36}

P(A \ occurs \ before \ B )=P[A \or (C\cap A) \or (C\cap C\cap CA)....]

                                                  =P(A) +P(C\cap A)+P (C\cap C\cap CA)....

                                                  =P(A) +P(C).P(A)+P (C)^{2}P(A)....

                                                    =\frac{P(A)}{1-P(C)}=\frac{\frac{1}{9}}{1-\frac{13}{18}}=\frac{1}{9} \times \frac{18}{5}=\frac{2}{5}

 


Option 1)

\frac{2}{5}

This option is correct

Option 2)

\frac{3}{7}

This option is incorrect

Option 3)

\frac{3}{13}

This option is incorrect

Option 4)

None of these

This option is incorrect

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