Find the probability of a $4$ turning up at least once in two tosses of a fair die.

The probability that a man will be alive $25$ years hence is $0.3$ and the probability that his wife will be alive $25$ years hence is $0.4$. Find the probability that $25$ years hence, at least $1$ of them will be alive.

For any event $A$,which of the following is true?

For independent events $A_1, A_2, \dots, A_n$, $P(A_i) = \frac{1}{i + 1}$ for $i = 1, 2, \dots, n$. Then the probability that none of the events will occur is:

$A$ husband and wife appear in an interview for $2$ vacancies in the same post. The probability of the husband's selection is $\frac{1}{7}$ and that of the wife's is $\frac{1}{5}$. What is the probability that only $1$ of them will be selected?

$A$ determinant is chosen at random from the set of all determinants of order $2$ with elements $0$ or $1$ only. The probability that the determinant chosen is non-zero is