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 coin is tossed. If it shows a tail, we draw a ball from a box which contains $2$ red and $3$  black balls. If it shows head, we throw a die. Find the sample space for this experiment.

Consider the set of all $7-$digit numbers formed by the digits $0,1,2,3,4,5,6$, each chosen exactly once. If a number is randomly drawn from this set, the probability that it is divisible by $4$ is

Three coins are tossed. Describe Three events which are mutually exclusive but not exhaustive.

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 not a black card.