$A$ die is thrown. Find the probability of the following event: $A$ number less than $6$ will appear.

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

$A$ coin is tossed and a dice is rolled. The probability that the coin shows the head and the dice shows $6$ is

One card is drawn from a well-shuffled deck of $52$ cards. If each outcome is equally likely,calculate the probability that the card will be a diamond but not an ace.

$A$ die is thrown. Describe the following events: $A$: a number less than $7$,$B$: a number greater than $7$,$C$: a multiple of $3$. Find $B \cup C$.

$A$ 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