A husband and a wife appear in an interview for two vacancies in the same post. The probability of husband's selection is $\frac{1}{7}$ and that of wife's selection is $\frac{1}{5}$. What is the probability that both of them will be selected?

A husband and a wife appear in an interview for two vacancies in the same post. The probability of husband's selection is $\frac{1}{7}$ and that of wife's selection is $\frac{1}{5}$. What is the probability that none of them will be selected ?

A husband and a wife appear in an interview for two vacancies in the same post. The probability of husband's selection is $\frac{1}{7}$ and that of wife's selection is $\frac{1}{5}$. What is the probability that only one of them will be selected ? 

A husband and a wife appear in an interview for two vacancies in the same post. The probability of husband's selection is $\frac{1}{7}$  and that of wife's selection is $\frac{1}{5}$. What is the probability that at least one of them will be selected ?

A machine operates if all of its three components function. The probability that the first component fails during the year is $0.14$, the probability that the second component fails is $0.10$ and the probability that the third component fails is $0.05$. What is the probability that the machine will fail during the year?

A speaks truth in 60% of the cases, while B in 40% of the cases. In what percent of cases are they likely to contradict each other in stating the same fact?

Ten Tickets are numbered $1$ to $10$. Two tickets are drawn one after the other at random. Find the probability that the number on one of the tickets is a multiple of $5$ and the other a multiple of $4$ when the tickets are drawn without replacement.

Ten Tickets are numbered $1$ to $10$. Two tickets are drawn one after the other at random. Find the probability that the number on one of the tickets is a multiple of $5$ and the other a multiple of $4$ when the tickets are drawn with replacement.

A bag contains $5$ red discs and $4$ blue discs. If $3$ discs are drawn from the bag without replacement, then find the probability that all three are blue.