Mr. A has six children and atleast one child is a girl, then probability that Mr. A has $3$ boys and $3$ girls, is 

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

There are four machines and it is known that exactly two of them are faulty. They are tested, one by one, is a random order till both the faulty machines are identified. Then the probability that only two tests are needed is

A bag contains $4$ white, $5$ red and $6$ black balls. If two balls are drawn at random, then the probability that one of them is white is

Let $A$ denote the event that a $6 -$digit integer formed by $0,1,2,3,4,5,6$ without repetitions, be divisible by $3 .$ Then probability of event $A$ is equal to :

An unbiased coin is tossed eight times. The probability of obtaining at least one head and at least one tail is