Let X and Y be two exponentially distributed and independent random variables with mean $$\alpha $$ and $$\beta $$, respectively. If Z = min (X, Y), then the mean of Z is given by

Consider two events $${{E_1}}$$ and $${{E_2}}$$ such that probability of $${{E_1}}$$, Pr [$${{E_1}}$$] = 1/2, probability of $${{E_2}}$$, Pr[$${{E_2}}$$ = 1/3, and probability of $${{E_1}}$$ and $${{E_2}}$$, $$\left[ {{E_1}\,\,or\,\,{E_2}} \right]$$ = 1/5. Which of the following statements is /are true?

The probability that the top and bottom cards of a randomly shuffled deck are both access is

A bag contains 10 white balls and 15 black balls. Two balls drawn in succession. The probability that one of them is black the other is white is