$A$ 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. 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

$A$ party of $23$ persons take their seats at a round table. The odds against two specific persons sitting together are

If the probability of $A$ failing an exam is $1/5$ and the probability of $B$ failing is $3/10$,what is the probability that either $A$ or $B$ fails?

If $A$ and $B$ are independent events such that odds in favour of $A$ is $2:3$ and odds against $B$ is $4:5$,then $P(A \cap B)=$

In class $XI$ of a school,$40\%$ of the students study Mathematics and $30\%$ study Biology. $10\%$ of the class study both Mathematics and Biology. If a student is selected at random from the class,find the probability that they will be studying Mathematics or Biology.