Q.Two dice are thrown simultaneously. Then the probability of getting two numbers whose product is even is A) $\frac{3}{4}$ B) $\frac{1}{4}$ C) $\frac{5}{7}$ D) $\frac{1}{2}$

From the classical definition, a set of properties follow that are used to manipulate probabilities without returning to first principles every time: $P(A')=1-P(A)$ (complement rule); $0\le P(A)\le1$ for every event; $P(\phi)=0$ for the impossible event and $P(S)=1$ for the certain event; probabilities add over mutually exclusive events, $P(A_1\cup A_2)=P(A_1)+P(A_2)$ when $A_1\cap A_2=\phi$, extending to any number of pairwise mutually exclusive events; if $A\subseteq B$ then $P(A)\le P(B)$ and $P(A'\cap B)=P(B)-P(A)$; and for any two events, $P(A\cap B')=P(A)-P(A\cap B)$. These properties are the toolkit combined in every subsequent proof in the chapter, including the addition theorem and the independence theorems.