$2$ persons $A$ and $B$ throw a die alternately until $1$ of them gets a '$6$' and wins the game. Find the probability of $B$ winning.

Two dice are thrown simultaneously. What is the probability of obtaining a multiple of $2$ on one of them and a multiple of $3$ on the other?

Study the given information carefully to answer the question that follows. An urn contains $4$ green,$5$ blue,$2$ red,and $3$ yellow marbles. If $8$ marbles are drawn at random,what is the probability that there are equal numbers of marbles of each colour?

One bag contains $4$ white balls and $2$ black balls; another contains $3$ white balls and $5$ black balls. If one ball is drawn from each bag,find the probability that both are white.

An urn contains $10$ green,$12$ yellow,and $11$ white balls. What is the probability that when $2$ balls are selected,both are green?

Two cards are drawn from a pack of $52$ cards. What is the probability that at least one of the cards drawn is an ace?