An examination paper has 150 multiple-choice questions of one mark each, with each question having four choices. Each incorrect answer fetches-0.25 mark. Suppose 1000 students choose all their answers randomly with uniform probability. The sum total of the expected marks obtained all these students is

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