When a pair of dice is thrown,what is the probability of getting an even number on each die?

$A$ and $B$ toss a coin alternatively,the first to show a head being the winner. If $A$ starts the game,the chance of his winning is

Three coins are tossed once. Find the probability of getting $3$ tails.

From $10,000$ lottery tickets numbered from $1$ to $10,000$,one ticket is drawn at random. What is the probability that the number marked on the drawn ticket is divisible by $20$?

Suppose that a die (with faces marked $1$ to $6$) is loaded in such a manner that for $K = 1, 2, 3, 4, 5, 6$,the probability of the face marked $K$ turning up when the die is tossed is proportional to $K$. The probability of the event that the outcome of a toss of the die will be an even number is equal to

$A$ problem in statistics is given to three students $A, B$ and $C$. Their probabilities of solving the problem are $\frac{1}{2}, \frac{1}{3}$ and $\frac{1}{4}$ respectively. If all of them try independently,then the probability that the problem is solved is