1. ## Probability-coin tossing

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

2. 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

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.

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

4. Originally Posted by senshiv
hey why its 1/8+ 1/8
it shud be 1/8 only
Same outcomes => 3 heads OR 3 tails.