Four persons $A$, $B$, $C$ and $D$ throw an unbiased die, turn by turn, in succession till one gets an even number and wins the game. What is the probability that $A$ wins if $A$ begins?

Let $A$ and $B$ be independent events such that $P(A)=p$ and $P(B)=2p$. The largest value of $p$, for which $P(\text{exactly one of } A, B \text{ occurs}) = \frac{5}{9}$, is:

$A$ 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:

In a throw of a dice,the probability of getting a $1$ in an even number of throws is:

Choose a number $n$ uniformly at random from the set $\{1, 2, \ldots, 100\}$. Choose one of the first seven days of the year $2014$ at random and consider $n$ consecutive days starting from the chosen day. What is the probability that among the chosen $n$ days,the number of Sundays is different from the number of Mondays?

$A$ and $B$ are independent events with $P(A)=\frac{1}{4}$ and $P(A \cup B)=2 P(B)-P(A)$,then $P(B)$ is