$A$ lot consists of $12$ good pencils,$6$ with minor defects,and $2$ with major defects. $A$ pencil is chosen at random. The probability that this pencil is not defective is

If $P(A) = \frac{1}{2}$,$P(B) = \frac{1}{3}$ and $P(A \cap B) = \frac{1}{4}$,then the value of $P(A' \cap B')$ is

$A$ dice is thrown twice. The probability of getting $4, 5$ or $6$ in the first throw and $1, 2, 3$ or $4$ in the second throw is

When a pair of dice is thrown,what is the probability of getting an even number on each die?

The probability of drawing a white ball from a bag containing $3$ black balls and $4$ white balls 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 $\leq 5$.
State true or false: (give reason for your answer)
Statement: $A', B', C$ are mutually exclusive and exhaustive.