$A$ and $B$ are two independent events such that $P(A) = 1/2$ and $P(B) = 1/3$. Then $P$ (neither $A$ nor $B$) is equal to

$A$ bag contains $4$ white and $3$ red balls. Two draws of one ball each are made without replacement. Then the probability that both the balls are red is (in $/7$)

The probabilities of winning the race by two athletes $A$ and $B$ are $\frac{1}{5}$ and $\frac{1}{4}$ respectively. The probability of winning by neither of them is:

Two dice are thrown simultaneously. What is the probability of obtaining a sum of the numbers less than $11$?

Let $A, B,$ and $C$ be three mutually independent events. Consider the two statements $S_1$ and $S_2$:
$S_1: A$ and $B \cup C$ are independent.
$S_2: A$ and $B \cap C$ are independent.
Then:

An urn contains $6$ blue,$4$ red,$3$ green,and $2$ yellow marbles. If three marbles are picked at random,what is the probability that $2$ are red and $1$ is green?