$A$ box contains $8$ red and $7$ black balls. If two balls are drawn at random,the probability that both balls are of the same color is ...... .

There are $10$ bulbs in a room,out of which $4$ are defective. If $3$ bulbs are chosen at random,what is the probability that the room will be illuminated? (The room is illuminated if at least one bulb is good.)

Let $X = \{(x, y) \in \mathbb{Z} \times \mathbb{Z} : \frac{x^2}{8} + \frac{y^2}{20} < 1 \text{ and } y^2 < 5x\}$. Three distinct points $P, Q,$ and $R$ are randomly chosen from $X$. Then the probability that $P, Q,$ and $R$ form a triangle whose area is a positive integer is

$A$ box contains $12$ balls,of which $4$ are red,$5$ are green,and $3$ are white. If $3$ balls are drawn at random simultaneously from the box,then the probability that exactly $2$ balls have the same colour is

Out of $21$ tickets marked with numbers from $1$ to $21$,three are drawn at random. The chance that the numbers on them are in $A.P.$ is

Nine balls are drawn simultaneously from a bag containing $5$ white and $7$ black balls. The probability of drawing $3$ white and $6$ black balls is: