$A$ 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

For two independent events $A$ and $B$,which of the following is true?

If two cards are drawn at random simultaneously from a pack of $52$ playing cards, then the probability of getting a face card and a spade card other than the face card is:

Two decks of playing cards are well shuffled and $26$ cards are randomly distributed to a player. Then, the probability that the player gets all distinct cards is

$A$ and $B$ are two independent events of a random experiment and $P(A) > P(B)$. If the probability that both $A$ and $B$ occur is $\frac{1}{6}$ and the probability that neither of them occurs is $\frac{1}{3}$,then the probability of the occurrence of $B$ is

Two persons $A$ and $B$ are throwing an unbiased six-faced dice alternatively,with the condition that the person who throws $3$ first wins the game. If $A$ starts the game,then the probabilities of $A$ and $B$ winning the game are,respectively: