A bag contains twelve pairs of socks and four socks are picked up at random. The probability that there is at least one pair is equal to

A bag contains $6$ red, $5$ white and $4$ black balls. Two balls are drawn. The probability that none of them is red, is

A purse contains $4$ copper coins $\& \, 3$ silver coins, the second purse contains $6$ copper coins $\& \,2$ silver coins. If a coin is drawn out of one of these purses, then the probability that it is a copper coin is :-

$3$ numbers are chosen from first $15$ natural numbers, then probability that the numbers are in arithmetic progression

In a regular $15$ -sided polygon with all its diagonals drawn, a diagonal is chosen at random. The probability that it is neither a shortest diagonal nor a longest diagonal is

A man draws a card from a pack of $52$ playing cards, replaces it and shuffles the pack. He continues this processes until he gets a card of spade. The probability that he will fail the first two times is