In the following experiment specify appropriate sample space.

A person is noting down the number of accidents along a busy highway during a year.

Two dice are thrown and the sum of the numbers which come up on the dice is noted. Let us consider the following events associated with this experiment

$\mathrm{A}:$ 'the sum is even'

$\mathrm{B}:$ 'the sum is a multiple of $3^{\text{'}}$

$\mathrm{C}:$ 'the sum is less than $4\text{'}$

$\mathrm{D}:$ 'the sum is greater than $11\text{'}$

Which pair of these events are mutually exclusive?

If sample space $\mathrm{S}=\left\{w_1,w_2,w_3,w_4,w_y,w_6,w_7\right]$, then which of the following assignments of probabilities are valid?

$\begin{array}{|cccccccc|}\hline \text{ Outcomes }& w_1& w_2& w_3& w_4& w_5& w_6& w_7\\ \left(i\right)& 0.1& 0.01& 0.05& 0.03& 0.01& 0.2& 0.6\\ \left(ii\right)& \frac{1}{7}& \frac{1}{7}& \frac{1}{7}& \frac{1}{7}& \frac{1}{7}& \frac{1}{7}& \frac{1}{7}\\ \left(iii\right)& 0.1& 0.2& 0.3& 0.4& 0.5& 0.6& 0.7\\ \left(iv\right)& -0.1& 0.2& 0.3& 0.4& -0.2& 0.1& 0.3\\ \left(v\right)& \frac{1}{14}& \frac{2}{14}& \frac{3}{14}& \frac{4}{14}& \frac{5}{14}& \frac{6}{14}& \frac{15}{14}\\ \hline\end{array}$