$A$ card is drawn at random from a pack of cards. What is the probability that the drawn card is neither a heart nor a king?

There are $10$ pairs of shoes in a cupboard from which $4$ shoes are picked at random. The probability that there is at least one pair is

$A$ person draws a card from a pack of playing cards,replaces it and shuffles the pack. He continues doing this until he draws a spade. The chance that he will fail in the first two attempts is

$2$ dice are thrown. Find the probability of getting a sum less than $6$.

The probabilities of a student getting $I, II$ and $III$ division in an examination are respectively $\frac{1}{10}, \frac{3}{5}$ and $\frac{1}{4}$. The probability that the student fails in the examination is

From a group of $7$ men and $4$ ladies,a committee of $6$ persons is formed. What is the probability that the committee contains exactly $2$ ladies?