Lifetime of an electric bulb is a random variable with density $$f\left( x \right) = k{x^2},$$ where $$x$$ is measured in years. If the minimum and maximum lifetimes of bulb are $$1$$ and $$2$$ years respectively, then the value of $$k$$ is ________.

A fair coin is tossed till a head appears for the first time. The probability that the number of required tosses is odd, is

A fair coin is tossed $$3$$ times in succession. If the first toss produces a head, then the probability of getting exactly two heads in three tosses is