Four fair coins are tossed simultaneously. The probability that at least one head and one tail turn up is

Seven (distinct) car accidents occurred in a week. What is the probability that they all occurred on the same day ?

$${{E_1}}$$ and $${{E_2}}$$ are events in a probability space satisfying the following constraints:
$$ \bullet $$ $$\Pr \,\,({E_1}) = \Pr \,({E_2})$$
$$ \bullet $$ $$\Pr \,\,({E_1}\, \cup {E_2}) = 1$$
$$ \bullet $$ $${E_1}$$ & $${E_2}$$ are independent

The value of Pr ($${E_1}$$), the probability of the event $${E_1}$$, is

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