A bag contains $5$ white, $7$ red and $8$ black balls. If four balls are drawn one by one without replacement, what is the probability that all are white

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. If first shows $5$, then the probability that the sum of the numbers appears on both is $8$ or more than $8$, is

For any event $A$

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 $\leq 5$

State true or false $:$ (give reason for your answer)

Statement : $A=B^{\prime}$