$A$ 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:

$A$ 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 $n$?

Two natural numbers are chosen at random from $1$ to $100$ and are multiplied. If $A$ is the event that the product is an even number and $B$ is the event that the product is divisible by $4$,then $P(A \cap \bar{B})=$

$U_1, U_2, U_3$ are three urns. $U_1$ contains $5$ red,$3$ white,$2$ black balls; $U_2$ contains $4$ red,$4$ white,$2$ black balls and $U_3$ contains $3$ red,$4$ white,$3$ black balls. If a ball is chosen at random from an urn chosen at random,then the probability of not getting a black ball is

In a random experiment,a fair die is rolled until two fours are obtained in succession. The probability that the experiment will end in the fifth throw of the die is equal to

$A$ player $X$ has a biased coin whose probability of showing heads is $p$ and a player $Y$ has a fair coin. They start playing a game with their own coins and play alternately. The player who throws a head first is a winner. If $X$ starts the game,and the probability of winning the game by both the players is equal,then the value of $p$ is