$A$ 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 ...... .

In a shoe rack,there are $4$ pairs of shoes. If $4$ shoes are drawn one after the other at random without replacement,what is the probability of getting at least one correct pair of shoes among the four shoes drawn?

$3$ balls are drawn one after the other without replacement from an urn containing $4$ red, $5$ blue and $6$ yellow balls. The probability of getting three different coloured balls is

If two numbers $a$ and $b$ are chosen from the first $30$ natural numbers,what is the probability that $a^2 - b^2$ is divisible by $3$?

Given that a throw of three unbiased dice shows different faces,what is the probability that their total is eight?

In a consignment of $15$ articles,it is found that $3$ are defective. If a sample of $5$ articles is chosen at random from it,then the probability of having $2$ defective articles is