Two dice are thrown simultaneously. The probability of getting the sum $2$,$8$,or $12$ is

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 true or false: (give reason for your answer)
Statement: $A$ and $B$ are mutually exclusive.

When a die is thrown twice,what is the probability of getting $4, 5,$ or $6$ on the first throw and $1, 2, 3,$ or $4$ on the second throw?

The probability that Krishna will be alive in $10$ years is $7/15$ and the probability that Hari will be alive in $10$ years is $7/10$. What is the probability that both will die within the next $10$ years (in $/150$)?

The probability of obtaining an even prime number on each die,when a pair of dice is rolled 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 black card (i.e.,a club or a spade).