Two cards are drawn without replacement from a well-shuffled pack. Find the probability that one of them is an ace of heart.

$A$ six-faced die is biased such that it is twice as likely to show an even number as an odd number when thrown. If it is thrown twice, what is the probability that the sum of the two numbers obtained is even?

If $E$ and $F$ are events with $P(E) \le P(F)$ and $P(E \cap F) > 0,$ then

If four persons are chosen at random from a group of $3$ men,$2$ women,and $4$ children,then the probability that exactly two of them are children is:

One bag contains $5$ white and $3$ black balls and a second bag contains $2$ white and $4$ black balls. One ball is drawn from the first bag and placed unseen in the second bag. What is the probability that a ball now drawn from the second bag is black?

Seven white balls and three black balls are randomly placed in a row. The probability that no two black balls are placed adjacently equals