A box contains $24$ identical balls, of which $12$ are white and $12$ are black. The balls are drawn at random from the box one at a time with replacement. The probability that a white ball is drawn for the $4^{th}$ time on the $7^{th}$ draw is

A bag contains $6$ white and $4$ black balls. A die is rolled once and the number of balls equal to the number obtained on the die are drawn from the bag at random. The probability that all the balls drawn are white is:

Out of $13$ applicants for a job, there are $5$ women and $8$ men. It is desired to select $2$ persons for the job. The probability that at least one of the selected persons will be a woman is

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

Two squares are chosen at random on a chessboard (see figure). The probability that they have a side in common is :

Each of the persons $\mathrm{A}$ and $\mathrm{B}$ independently tosses three fair coins. The probability that both of them get the same number of heads is :