Three $6$-faced dice are thrown together. The probability that exactly two dice show the same number on them is:

The probabilities of a problem being solved by two students are $\frac{1}{2}$ and $\frac{1}{3}$ respectively. What is the probability that the problem is solved?

Study the given information carefully and answer the questions that follow: $A$ basket contains $4$ red,$5$ blue and $3$ green marbles. If $3$ marbles are picked at random,what is the probability that either all are green or all are red?

If $4\,P(A) = 6\,P(B) = 10\,P(A \cap B) = 1,$ then $P\left( \frac{B}{A} \right) = $

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 $4$ marbles are drawn at random,what is the probability that $2$ are blue and $2$ are red?

When two dice are rolled,what is the probability that the sum of the numbers appearing is a multiple of $3$?