Three dice are thrown. The sum of the numbers is $15$. What is the chance of getting $4$ on the first die?

$A$ determinant is chosen at random from the set of all determinants of order $2$ with elements $0$ or $1$ only. The probability that the value of the determinant chosen is positive is:

If $P(A) = 2/3$,$P(B) = 1/2$ and $P(A \cup B) = 5/6$,then events $A$ and $B$ are

Two numbers $a$ and $b$ are chosen at random from the set of first $30$ natural numbers. The probability that $a^2 - b^2$ is divisible by $3$ is

$A$ bag contains $3$ red,$7$ white,and $4$ black balls. If three balls are drawn from the bag,the probability that all of them are of the same color is:

$A$ bag contains $5$ white,$7$ black and $4$ red balls. Three balls are drawn from the bag at random,then the probability that all the three balls are white,is