The probability of obtaining an even prime number on each die when a pair of dice is rolled is

$A$ and $B$ throw a pair of dice alternately and they note the sum of the numbers appearing on the dice. $A$ wins if he throws $6$ before $B$ throws $7$,and $B$ wins if he throws $7$ before $A$ throws $6$. If $A$ begins,the probability of $A$ winning is:

Two persons $A$ and $B$ throw a fair die (six-faced cube with faces numbered from $1$ to $6$) alternately,starting with $A$. The first person to get an outcome different from the previous one thrown by the opponent wins. The probability that $B$ wins is:

$P$ 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 $\%$)?

If two unbiased six-faced dice are thrown simultaneously until a sum of either $7$ or $11$ occurs,then the probability that $7$ comes before $11$ is

$A$ coin is tossed $m + n$ times,where $m \ge n.$ The probability of getting at least $m$ consecutive heads is