If $A$ and $B$ are two events such that $P\,(A \cup B)\, + P\,(A \cap B) = \frac{7}{8}$ and $P\,(A) = 2\,P\,(B),$ then $P\,(A) = $

For an event, odds against is $6 : 5$. The probability that event does not occur, is

In an entrance test that is graded on the basis of two examinations, the probability of a randomly chosen student passing the first examination is $0.8$ and the probability of passing the second examination is $0.7 .$ The probability of passing at least one of them is $0.95 .$ What is the probability of passing both ?

Let $A$ and $B$ are 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

If $A$ and $B$ are two events such that $P(A) = \frac{1}{2}$ and $P(B) = \frac{2}{3},$ then

If the odds against an event be $2 : 3$, then the probability of its occurrence is