The odds against solving a problem by $A$ and $B$ are $3:2$ and $2:1$ respectively. The probability that the problem will be solved is:

The odds against a person who is $40$ years old living until he is $70$ are $8$ to $5$,and the odds against another person who is $50$ years old living until he is $80$ are $4$ to $3$. Find the probability that exactly one of them will be alive $30$ years from now.

$A$ card is drawn from a pack of $52$ cards. $A$ gambler bets that it is a spade or an ace. What are the odds against his winning this bet?

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.

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 $P(A \cup B)$.

Two dice are thrown simultaneously. The probability that the sum is odd or less than $7$ or both is: