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
$\frac{11}{16}$
$\frac{13}{16}$
$\frac{9}{16}$
$\frac{15}{16}$
If $10$ different balls are to be placed in $4$ distinct boxes at random, then the probability that two of these boxes contain exactly $2$ and $3$ balls is
In a regular $15$ -sided polygon with all its diagonals drawn, a diagonal is chosen at random. The probability that it is neither a shortest diagonal nor a longest diagonal is
Find the probability that when a hand of $7$ cards is drawn from a well shuffled deck of $52$ cards, it contains atleast $3$ Kings.
A bag has $13$ red, $14$ green and $15$ black balls. The probability of getting exactly $2$ blacks on pulling out $4$ balls is ${P_1}$. Now the number of each colour ball is doubled and $8$ balls are pulled out. The probability of getting exactly $4$ blacks is ${P_2}.$ Then
Two friends $A$ and $B$ have equal number of daughters. There are three cinema tickets which are to be distributed among the daughters of $A$ and $B$. The probability that all the tickets go to daughters of $A$ is $1/20$. The number of daughters each of them have is