Probability-coin tossing

**senshiv** · Apr 28th 2010, 02:33 AM

3 persons play a game by tossing a fair coin each independently. The game ends in a trial if all of them get the same outcome in that trial,otherwise they continue to the next trial. what is the probability that the game end in an even number of trials.
options are 1)2/7 2)3/7 3) 1/2 4) 4/7

Please help me out in this ques asap.its very urgent

**mr fantastic** · Apr 28th 2010, 04:52 AM

Originally Posted by senshiv

3 persons play a game by tossing a fair coin each independently. The game ends in a trial if all of them get the same outcome in that trial,otherwise they continue to the next trial. what is the probability that the game end in an even number of trials.
options are 1)2/7 2)3/7 3) 1/2 4) 4/7

Please help me out in this ques asap.its very urgent

Probability of success = 1/8 + 1/8 = 1/4.

Pr(X = even) = Pr(X = 2) + Pr(X = 4) + Pr(X = 6) + ....

$= \left( \frac{3}{4} \right) \cdot \left( \frac{1}{4} \right) + \left( \frac{3}{4} \right)^3 \cdot \left( \frac{1}{4} \right) + \left( \frac{3}{4} \right)^5 \cdot \left( \frac{1}{4} \right) + ....$

$= \frac{1}{4} \cdot \frac{3}{4} \left( 1 + \left( \frac{3}{4} \right)^2 +\left( \frac{3}{4} \right)^4 + .... \right)$

and the expression inside the brackets is an infinite geometric series whose sum you should be able to get.

**senshiv** · Apr 28th 2010, 06:20 AM

hey why its 1/8+ 1/8
it shud be 1/8 only

**mr fantastic** · Apr 28th 2010, 06:31 AM

Originally Posted by senshiv

hey why its 1/8+ 1/8
it shud be 1/8 only

Same outcomes => 3 heads OR 3 tails.

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