$A$ card is drawn from a pack of $52$ cards. If $A =$ card is of diamond,$B =$ card is an ace,and $A \cap B =$ card is the ace of diamond,then events $A$ and $B$ are

If $A$ and $B$ are events such that $P(A \cup B) = 3/4,$ $P(A \cap B) = 1/4,$ and $P(\bar{A}) = 2/3,$ then $P(\bar{A} \cap B)$ is

$A$ box contains $4$ white pens and $2$ black pens. Another box contains $3$ white pens and $5$ black pens. If one pen is selected from each box,then the probability that both the pens are white is equal to

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: $A = B^{\prime}$

$A$ and $B$ toss a coin alternatively,the first to show a head being the winner. If $A$ starts the game,the chance of his winning is

Two fair dice are rolled. The probability of the sum of digits on their faces being greater than or equal to $10$ is