Ravi and Rashmi each hold $2$ red cards and $2$ black cards (all four red and all four black cards are identical). Ravi picks a card at random from Rashmi and then Rashmi picks a card at random from Ravi. This process is repeated a second time. Let $p$ be the probability that both have all $4$ cards of the same colour. Then,$p$ satisfies

Two fair dice,each with faces numbered $1, 2, 3, 4, 5$ and $6$,are rolled together and the sum of the numbers on the faces is observed. This process is repeated until the sum is either a prime number or a perfect square. Suppose the sum turns out to be a perfect square before it turns out to be a prime number. If $p$ is the probability that this perfect square is an odd number,then the value of $14p$ is . . . . .

$A$ locker can be opened by dialing a fixed three-digit code (between $000$ and $999$). $A$ stranger who does not know the code tries to open the locker by dialing three digits at random. The probability that the stranger succeeds at the $k^{th}$ trial is

$A$ biased die is marked with numbers $2, 4, 8, 16, 32, 32$ on its faces. The probability of getting a face with mark $n$ is $\frac{1}{n}$. If the die is thrown thrice,then the probability that the sum of the numbers obtained is $48$ is:

$A$ bag contains $n + 1$ coins. Among these coins,one coin has heads on both sides,while all other coins are fair. $A$ coin is chosen at random from the bag. If the probability of getting a head when the chosen coin is tossed is $7/12$,what is the value of $n$?

Five different books are to be distributed among four students randomly. The probability that each child gets at least one book is