When two dice are rolled,what is the probability that at least one face shows a six?

If $A, B, C$ are three events of a sample space such that $P(B)=\frac{3}{2} P(A)$ and $P(C)=\frac{1}{2} P(B)$, then which of the following is correct?

If $A, B, C$ are three mutually exclusive and exhaustive events of an experiment such that $P(A)=2 P(B)=3 P(C)$,then $P(B)$ is equal to

Let $M$ be the maximum value of the product of two positive integers when their sum is $66$. Let the sample space $S = \{x \in \mathbb{Z} : x(66 - x) \geq \frac{5}{9} M\}$ and the event $A = \{x \in S : x \text{ is a multiple of } 3\}$. Then $P(A)$ is equal to

$A$ coin is tossed. If it shows head,we draw a ball from a bag consisting of $3$ blue and $4$ white balls; if it shows tail,we throw a die. Describe the sample space of this experiment.

The probabilities of solving a specific problem independently by $A$ and $B$ are $\frac{1}{2}$ and $\frac{1}{3}$ respectively. If both try to solve the problem independently,find the probability that exactly one of them solves the problem.