Three fair cubical dice are thrown simultaneously. The probability that all three dice have the same number of dots on the faces showing up is (up to third decimal place) _________.

$$500$$ students are taking one or more courses out of chemistry, physics and Mathematics. Registration records indicate course enrolment as follows: chemistry $$(329)$$, physics $$(186)$$, Mathematics $$(295)$$, chemistry and physics $$(83)$$, chemistry and Mathematics $$(217)$$, and physic and Mathematics $$(63)$$, How many students are taking all $$3$$ subjects?

The second moment of a Poisson-distributed random variables is $$2.$$ The mean of the random variable is _______.

Let the random variable $$X$$ represent the number of times a fair coin needs to be tossed till two consecutive heads appear for the first time. The expectation of $$X$$ is ________.