It is estimated that the average number of events during a year is three. What is the probability of occurrence of not more than two events over a two-year duration? Assume that the number of events follow a poisson distribution.

If a random variable $$X$$ satisfies the poission's distribution with a mean value of $$2,$$ then the probability that $$X > 2$$ is

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