Let $E$ and $F$ be two independent events. The probability that both $E$ and $F$ happen is $\frac{1}{12}$ and the probability that neither $E$ nor $F$ happens is  $\frac{1}{2}$ , then a value of  $\frac{{P(E)}}{{P\left( F \right)}}$ is

Two dice are thrown. The events $A, B$ and $C$ are as follows:

$A:$ getting an even number on the first die.

$B:$ getting an odd number on the first die.

$C:$ getting the sum of the numbers on the dice $\leq 5$

Describe the events  $A$ but not $C$

Let $E _{1}, E _{2}, E _{3}$ be three mutually exclusive events such that $P \left( E _{1}\right)=\frac{2+3 p }{6}, P \left( E _{2}\right)=\frac{2- p }{8}$ and $P \left( E _{3}\right)$ $=\frac{1- p }{2}$. If the maximum and minimum values of $p$ are $p _{1}$ and $p _{2}$, then $\left( p _{1}+ p _{2}\right)$ is equal to.

Three coins are tossed once. Find the probability of getting no head.

On her vacations Veena visits four cities $(A,\,B ,\, C$ and $D$ ) in a random order. What is the probability that she visits $A$ first and $B$ last ?