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
$\frac{5}{{64}}$
$\frac{{27}}{{32}}$
$\frac{5}{{32}}$
$\frac{1}{2}$
If a party of $n$ persons sit at a round table, then the odds against two specified individuals sitting next to each other are
A bag has $13$ red, $14$ green and $15$ black balls. The probability of getting exactly $2$ blacks on pulling out $4$ balls is ${P_1}$. Now the number of each colour ball is doubled and $8$ balls are pulled out. The probability of getting exactly $4$ blacks is ${P_2}.$ Then
Word ‘$UNIVERSITY$’ is arranged randomly. Then the probability that both ‘$I$’ does not come together, 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
Suppose $n \ge 3$ persons are sitting in a row. Two of them are selected at random. The probability that they are not together is