If the probabilities of three independent events occurring are $p_1, p_2, p_3$,what is the probability that at least one of these events occurs?

Let $X_n = \{1, 2, 3, \ldots, n\}$ and let a subset $A$ of $X_n$ be chosen such that every pair of elements of $A$ differ by at least $3$. (For example,if $n = 5$,$A$ can be $\phi, \{2\}$ or $\{1, 5\}$ among others). When $n = 10$,let the probability that $1 \in A$ be $p$ and let the probability that $2 \in A$ be $q$. Then,

$A$ draws two cards with replacement from a pack of $52$ cards and $B$ throws a pair of dice. What is the chance that $A$ gets both cards of the same suit and $B$ gets a total of $6$?

If two cards are drawn at random simultaneously from a pack of $52$ playing cards, then the probability of getting a face card and a spade card other than the face card is:

If $n$ positive integers are taken at random and multiplied together,the probability that the last digit of the product is $2, 4, 6$ or $8$ is:

If $E_1, E_2, \ldots, E_n$ are independent events such that $P(E_r) = \frac{1}{1+r}$ for $r = 1, 2, \ldots, n$, then the probability that at least one of $E_1, E_2, \ldots, E_n$ happens is