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 $20$?

$A$ and $B$ throw a coin alternately till $1$ of them gets a head and wins the game. If $A$ starts the game,find the probability of $A$ winning.

If $P(A) = \frac{2}{3}$,$P(B) = \frac{4}{9}$ and $P(A \cap B) = \frac{14}{45}$,then find $P(A \cup B)$.

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

Suppose $n \ge 3$ persons are sitting in a row. Two of them are selected at random. The probability that they are not together is

In an entrance test,there are multiple-choice questions. There are four possible answers to each question,of which one is correct. The probability that a student knows the answer to a question is $90\%$. If he gets the correct answer to a question,then the probability that he was guessing is: