If a number is chosen at random from the set $\{1, 2, 3, \ldots, 100\}$,then the probability that the chosen number is a perfect cube is

The chances to fail in Physics are $20\%$ and the chances to fail in Mathematics are $10\%$. What are the chances to fail in at least one subject? ............ $\%$

Two dice are thrown. The events $A, B$ and $C$ are as follows:
$A:$ getting an even number on the first die.
$B:$ getting an odd number on the first die.
$C:$ getting the sum of the numbers on the dice $\leq 5$.
State whether the following statement is true or false and provide a reason:
Statement: $A = B^{\prime}$

Three students $A$,$B$ and $C$ are running a race. $A$ and $B$ have the same probability of winning and each is twice as likely to win as $C$. Then,the probability that $B$ or $C$ wins is equal to (assuming there are no ties)

$A$ non-zero integer $x$ is selected randomly from the set of integers $\{x \in Z \mid -25 \leq x \leq 25, x \neq 0\}$. The probability that $x + 6 \leq \frac{135}{x}$ is

If a leap year is selected at random,what is the chance that it will contain $53$ Tuesdays?