In a game, two players $$X$$ and $$Y$$ toss a coin alternately. Whoever gets a 'head' first, wins the game and the game is terminated. Assuming that players $$X$$ starts the game the probability of player $$X$$ winning the game is

If $$X$$ is a continuous random variable whose probability density function is given by $$$\,\,\,f\left( x \right) = \left\{ {\matrix{ {k\left( {5x - 2{x^2}} \right),} & {0 \le x \le 2} \cr {0,} & {Otherwise} \cr } } \right.\,\,\,\,$$$
Then $$P\left( {x > 1} \right)$$ is

Two cards are drawn at random in succession with replacement from a deck of $$52$$ well shuffled cards Probability of getting both 'Aces' is