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).

A box contains $$2$$ fifty paise coins, $$5$$ twenty five paise coins and a certain fixed number $$N\,\,\left( { \ge 2} \right)$$ of ten and five paise coins. Five coins are taken out of the box at random. Find the probability that the total value of these $$5$$ coins is less than one rupee and fifty paise.

A man takes a step forward with probability $$0.4$$ and backwards with probability $$0.6$$ Find the probability that at the end of eleven steps he is one step away from the starting point.

A lot contains $$20$$ articles. The probability that the lot contains exactly $$2$$ defective articles is $$0.4$$ and the probability that the lot contains exactly $$3$$ defective articles is $$0.6$$. Articles are drawn from the lot at random one by one without replacement and are tested till all defective articles are found. What is the probability that the testing procedure ends at the twelth testing.