One of the two events must occur. If the chance of one is $\frac{2}{3}$ of the other,then the odds in favour of the other are

Let $A$ and $B$ be two independent events of an experiment. If $P(A) = 0.3$ and $P(A \cup B) = 0.8$,then find $P(A \to B)$,where $P(X)$ denotes the probability that statement $X$ is true.

When two dice are thrown once,find the odds against getting a sum of $7$ on the two dice.

What is the probability of drawing either a queen or a red card from a deck of $52$ cards?

Let $A$ and $B$ be two independent events. The probability that both $A$ and $B$ occur together is $1/6$ and the probability that neither of them occurs is $1/3$. The probability of occurrence of $A$ is

Suppose that $A, B, C$ are events such that $P(A) = P(B) = P(C) = \frac{1}{4}$,$P(AB) = P(CB) = 0$,and $P(AC) = \frac{1}{8}$. Then find $P(A \cup B)$.