Three coins are tossed together,then the probability of getting at least one head is

$A$ man and a woman appear in an interview for two vacancies in the same post. The probability of the man's selection is $1/4$ and that of the woman's selection is $1/3$. What is the probability that none of them will be selected?

Three randomly chosen non-negative integers $x, y$ and $z$ are found to satisfy the equation $x+y+z=10$. Then the probability that $z$ is even,is

The probabilities that $A$ and $B$ will die within a year are $p$ and $q$ respectively. Then,the probability that only one of them will be alive at the end of the year is

Let $S$ be the sample space of the random experiment of throwing simultaneously two unbiased dice and $E_k = \{(a, b) \in S : ab = k\}$. If $p_k = P(E_k)$, then which of the following is correct?

$A$ card is drawn at random from a well-shuffled pack of $52$ cards. The probability that it is a black card or a face card is