Two white and two black balls, kept in two bins, are arranged in four ways as shown below. In each arrangement, a bin has to be chosen randomly and only one ball needs to be picked randomly from the chosen bin. Which one of the following arrangements has the highest probability for getting a while ball picked?

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