A pair of fair dice is rolled together till a sum of either $$5$$ or $$7$$ is obtained. Then the probability that $$5$$ comes before $$7$$ is ...............

If the probability for $$A$$ to fail in an examination is $$0.2$$ and that for $$B$$ is $$0.3$$, then the probability that either $$A$$ or $$B$$ fails is $$0.5$$

If $$E$$ and $$F$$ are independent events such that $$0 < P\left( E \right) < 1$$ and $$0 < P\left( F \right) < 1,$$ then

Suppose the probability for A to win a game against B is $$0.4.$$ If $$A$$ has an option of playing either a "best of $$3$$ games" or a "best of $$5$$ games" match against $$B$$, which option should be choose so that the probability of his winning the match is higher ? (No game ends in a draw).