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  • Try this! In a random experiment, a fair die is rolled until two fours are obtained in succession. The probability that the experiment will end in the fifth throw of the die is equal to :

In a random experiment, a fair die is rolled until two fours are obtained in succession. The probability that the experiment will end in the fifth throw of the die is equal to : 

  • Option 1) 200/65

     

  • Option 2) 150/65

     

  • Option 3) 225/65

     

  • Option 4) 175/65

     

Answers (1)

best_answer

 

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.

 

 

 

Conditional Probability -

Let A and B be any two events such that B\neq \phi  or

n(B) = 0 or P(B) = 0 then P\left ( \frac{A}{B} \right ) denotes the conditional probability of occurrence of event A when B has already occured

 

-

P(---4)=P(4--44)+P(not \: 4--44)

                         =\frac{1}{6}\times \frac{5}{6}\times \frac{5}{6}\times \frac{1}{6}\times \frac{1}{6}+ \frac{5}{6}\times1\times\frac{5}{6}\times\frac{1}{6}\times\frac{1}{6}

                        =\frac{25}{6^{5}}+\frac{25}{6^{4}}

                        =\frac{175}{6^{5}}

 

 


Option 1)

 \frac{200}{6^{5}}

 

 

 

Option 2)

\frac{150}{6^{5}}

Option 3)

\frac{225}{6^{5}}

Option 4)

\frac{175}{6^{5}}

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