Home » Uncategorized » GATE 2015 EE - SET 1 -Question 29

# GATE 2015 EE - SET 1 -Question 29

Solution :

Probability of getting a 6 = $\frac{1}{6}$

Probability of A Winning is  = $\frac{1}{6}$

Probability of A losing is = 1 - $\frac{1}{6}$$\frac{5}{6}$

Probability of B winning is = $\frac{1}{6}$

Probability of  B losing is = $\frac{1}{6}$

If A starts the game , the probability of A winning ,

P(A) + $P(\bar{A})P(\bar{B})P(A)+P(\bar{A})P(\bar{B})P(\bar{A})P(\bar{B})P(A)$

$\frac{1}{6} + \frac{5}{6}* \frac{5}{6} *\frac{1}{6} +\frac{5}{6}* \frac{5}{6}* \frac{5}{6}* \frac{5}{6}* \frac{1}{6}*$+ ...................

$\frac{1}{6}\left [ 1+ \frac{5}{6}* \frac{5}{6}+\frac{5}{6}* \frac{5}{6}*\frac{5}{6}* \frac{5}{6}+....\right ]$

$\frac{1}{6}\left [1 + (\frac{5}{6}) ^{2}+(\frac{5}{6}) ^{4}+ .... \right ]$

$\left [ 1 + a^{2} +a^{4}+....\right ]$

$\Rightarrow$ $\left [ \frac{1}{1-a^{2}} \right ]$

a = $\frac{1}{6}$, r =$(\frac{5}{6})^{2}$ =$\frac{25 }{36}$

a = $\frac{1}{6}$ , r = a = $\frac{25}{36}$

$S_{\infty }$= $\frac{\frac{1}{6}}{1-\left ( \frac{25}{36} \right )}$

$\frac{\frac{1}{6}}{(\frac{36-25}{36})}$ = $\frac{6 }{11}$

Translate »