If two dice are thrown simultaneously then probability that $1$ comes on first dice is

Two cards are drawn without replacement from a well-shuffled pack. Find the probability that one of them is an ace of heart

A set $S$ contains $7$ elements. A non-empty subset $A$ of $S$ and an element $x$ of $S$ are chosen at random. Then the probability that $x \in A$ is

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 the $B \cup C$

For three non impossible events $A$, $B$ and $C$ $P\left( {A \cap B \cap C} \right) = 0,P\left( {A \cup B \cup C} \right) = \frac{3}{4},$ $P\left( {A \cap B} \right) = \frac{1}{3}$ and $P\left( C \right) = \frac{1}{6}$.

The probability, exactly one of $A$ or $B$ occurs but $C$ doesn't occur is 

A box containing $4$ white pens and $2$ black pens. Another box containing $3$ 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