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

$A$ bag contains $3$ black and $4$ white balls. Two balls are drawn one by one at random without replacement. The probability that the second drawn ball is white,is

$1$ bag contains $4$ white and $2$ black balls. Another bag contains $3$ white and $5$ black balls. If $1$ ball is drawn from each bag,find the probability that both balls are black.

$2$ persons $A$ and $B$ throw a die alternately until $1$ of them gets a '$6$' and wins the game. Find the probability of $B$ winning.

Six boys and six girls sit in a row randomly. What is the probability that the six girls sit together?

The probability that $A$ speaks the truth is $\frac{4}{5}$,while this probability for $B$ is $\frac{3}{4}$. Find the probability that they contradict each other when asked to speak on a fact.