$P$ 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 $\%$)?

Let $A$ denote the set of all $4$-digit natural numbers with no digit being $0$. Let $B \subset A$ consist of all numbers $x$ such that no permutation of the digits of $x$ gives a number that is divisible by $4$. Then the probability of drawing a number from $B$ with all even digits is

If the integers $m$ and $n$ are chosen at random between $1$ and $100$,then the probability that a number of the form $7^m + 7^n$ is divisible by $5$ equals

If the letters of the word $REGULATIONS$ are arranged in such a way that the relative positions of the letters of the word $GULATIONS$ remain the same,then the probability that there are exactly $4$ letters between $R$ and $E$ is

$A$ pair of fair dice is rolled together till a sum of either $5$ or $7$ is obtained. Then the probability that $5$ comes before $7$ is

Three screws are drawn at random from a lot of $50$ screws containing $5$ defective ones. The probability of the event that all $3$ screws drawn are non-defective,assuming that the drawing is $(a)$ with replacement and $(b)$ without replacement,is respectively: