Two fair dice are thrown. State the sample space and write the favourable outcomes for the following events.

$C$: Odd number on the first die.  

Two fair dice are thrown. State the sample space and write the favorable outcomes for the following event.

$D$: Even number on the first die.

Two fair dice are thrown. We have event

$A:$ Sum of numbers is divisible by $3$ or $4$

$B:$ Sum of numbers is $7$

Check whether events $A$ and $B$ are mutually exclusive and exhaustive. 

Two fair dice are thrown. State the sample space and write the favorable outcomes for the following two events $C$ and $D$. Also, check whether events are mutually exclusive and exhaustive. 

$C:$  an event that odd number occurs on first die

$D:$ an event that number on first die is an even number

A bag contains four cards marked as $5$, $6$, $7$ and $8$. Find the sample space if two cards are drawn at random with replacement. 

A bag contains four cards marked as $5$, $6$, $7$ and $8$. Find the sample space if two cards are drawn at random without replacement. 

A fair die is thrown two times. Find the probability that sum of the numbers on them is $5$.

A fair die is thrown two times. Find the probability that sum of the numbers on them is at least $8$.

A fair die is thrown two times. Find the probability that first throw gives a multiple of $2$ and second throw gives a multiple of $3$ .