The chance of getting a doublet with $2$ dice is

One card is drawn from each of two ordinary packs of $52$ cards. The probability that at least one of them is an ace of hearts 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 whether the following statement is true or false and provide a reason:
Statement: $A = B^{\prime}$

When three coins are tossed simultaneously,what is the probability of getting at least one head?

Let $A, B$ and $C$ be three events associated with sample space $S$. $A, B$ and $C$ are pairwise independent and $P(A)=P(B)=P(C)=P$. If all of them cannot occur simultaneously,then $P(A \cup B \cup C)$ is equal to

$A, B$ and $C$ are mutually exclusive events. If $P(A) = \frac{3x + 1}{3}$,$P(B) = \frac{1 - x}{4}$,and $P(C) = \frac{1 - 2x}{2}$,then the possible values of $x$ lie in the interval ...