The random variable $$X$$ takes on the values $$1,$$ $$2$$ (or) $$3$$ with probabilities $$\,{{2 + 5P} \over 5},{{1 + 3P} \over 5}\,\,$$ and $$\,\,{{1.5 + 2P} \over 5}\,\,$$ respectively the values of $$P$$ and $$E(X)$$ are respectively

The life of a bulb (in hours) is a random variable with an exponential distribution $$\,\,f\left( t \right) = \alpha {e^{ - \alpha t}},0 \le t \le \infty .\,\,\,$$ The probability that its value lies $$b/w$$ $$100$$ and $$200$$ hours is

Two dice are thrown simultaneously. The probability that the sum of numbers on both exceeds $$8$$ is