$A$ number is chosen at random from the first ten natural numbers. The probability that the number is odd and a perfect square is

$A$ box contains $6$ red marbles numbered from $1$ through $6$ and $4$ white marbles numbered $12$ through $15$. Find the probability that a marble drawn at random is white and odd-numbered.

If two numbers $x$ and $y$ are chosen one after the other at random with replacement from the set of numbers $\{1, 2, 3, \ldots, 10\}$,then the probability that $|x^2 - y^2|$ is divisible by $6$ is

The probabilities of $A, B,$ and $C$ solving a problem are $\frac{1}{3}, \frac{2}{7},$ and $\frac{3}{8}$ respectively. If all three try to solve the problem simultaneously,the probability that exactly one of them will solve it is:

The probability that a leap year selected randomly will have $53$ Sundays is

$A$ bag contains $3$ white,$3$ black and $2$ red balls. Three balls are drawn one by one without replacement. The probability that the third ball is red is: