An ordinary cube has four blank faces,one face marked $2$,and another marked $3$. The probability of obtaining a total of exactly $12$ in $5$ throws is:

$A$ pack of cards contains $4$ aces,$4$ kings,$4$ queens,and $4$ jacks. Two cards are drawn at random. The probability that at least one of these is an ace is:

Let $0 < P(A) < 1$,$0 < P(B) < 1$ and $P(A \cup B) = P(A) + P(B) - P(A)P(B).$ Then

$A$ and $B$ throw a die alternatively till one of them gets a '$6$' and wins the game. Find their respective probabilities of winning,if $A$ starts first.

If three boxes contain $3$ white and $1$ black,$2$ white and $2$ black,and $1$ white and $3$ black balls respectively,and one ball is chosen at random from each box,what is the probability of selecting $2$ white and $1$ black ball?

$P$ speaks truth in $70\%$ of the cases and $Q$ in $80\%$ of the cases. In what percent of cases are they likely to agree in stating the same fact (in $\%$)?