P and Q are playing a game in which they toss a biased coin alternately.the probability of Heads is 0.2. The game continous till head comes and person getting head wins out - find the probability that P wins if Q starts.

  • Option 1)

    \frac{1}{3}

  • Option 2)

    \frac{2}{3}

  • Option 3)

    \frac{5}{9}

  • Option 4)

    \frac{4}{9}

 

Answers (1)

Use the concept

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(P)=0.2\rightarrow winning

P(\bar{P})=0.8\rightarrow Loss

\therefore for\: winning \: Q

=0.2+0.8\times 0.8\times 0.2+-----\infty

=>\frac{0.2}{1-(0.8)^{2}}=\frac{0.2}{1-0.64}=\frac{0.2}{0.36}

\frac{20}{36}=\frac{5}{9}

\therefore winning\: chance\: for\: P=1-\frac{5}{9}

=\frac{4}{9}


Option 1)

\frac{1}{3}

Option is incorrect

Option 2)

\frac{2}{3}

Option is incorrect

Option 3)

\frac{5}{9}

Option is incorrect

Option 4)

\frac{4}{9}

Option is correct

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