Seven white balls and three black balls are randomly placed in a row. The probability that no two black balls are placed adjacently equals
$\frac{1}{2}$
$\frac{7}{{15}}$
$\frac{2}{{15}}$
$\frac{1}{3}$
A bag contains $3$ white and $5$ black balls. If one ball is drawn, then the probability that it is black, is
One of the two events must occur. If the chance of one is $\frac{{2}}{{3}}$ of the other, then odds in favour of the other are
From a group of $10$ men and $5$ women, four member committees are to be formed each of which must contain at least one woman. Then the probability for these committees to have more women than men, 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 :-
Fifteen persons among whom are $A$ and $B$, sit down at random at a round table. The probability that there are $4$ persons between $A$ and $B$, is