Two n bit binary stings, S1 and, are chosen randomly with uniform probability. The probability that the Hamming distance between these strings (the number of bit positions where the two strings different) is equal to d 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