In a box, there are $20$ cards, out of which $10$ are lebelled as $\mathrm{A}$ and the remaining $10$ are labelled as $B$. Cards are drawn at random, one after the other and with replacement, till a second $A-$card is obtained. The probability that the second $A-$card appears before the third $B-$card is
$\frac{11}{16}$
$\frac{13}{16}$
$\frac{9}{16}$
$\frac{15}{16}$
The number lock of a suitcase has $4$ wheels, each labelled with ten digits i.e., from $0$ to $9 .$ The lock opens with a sequence of four digits with no repeats. What is the probability of a person getting the right sequence to open the suitcase?
If $12$ identical balls are to be placed randomly in $3$ identical boxes, then the probability that one of the boxes contains exactly $3$ balls is
$3$ numbers are chosen from first $15$ natural numbers, then probability that the numbers are in arithmetic progression
Let $n$ be the number of ways in which $5$ boys and $5$ girls can stand in a queue in such a way that all the girls stand consecutively in the queue. Let $m$ be the number of ways in which $5$ boys and $5$ girls can stand in a queue in such a way that exactly four girls stand consecutively in the queue. Then the value of $\frac{m}{n}$ is
In a lottery $50$ tickets are sold in which $14$ are of prize. A man bought $2$ tickets, then the probability that the man win the prize, is