Functions are formed from the set $A=\left\{a_1, a_2, a_3\right\}$ to another set $B=\left\{b_1, b_2, b_3, b_4, b_5\right\}$. If a function is selected at random, then probability, that it is a non-one function is

$A$ and $B$ are two events of a random experiment such that $P(B)=0.4, P(A \cap \bar{B})=0.5, P(A \cup B)+P\left(\frac{B}{A \cup \bar{B}}\right)=1.15$ then $P(A)=$

There are two boxes each containing 10 balls. In each box, few of them are black balls and rest are white. A ball is drawn at random from one of the boxes and found that it is black. If the probability that the black ball drawn is from the second box is $\frac{1}{5}$, then number of black balls in the first box is

In a shelf there are three mathematics and two physics books. A student takes a book randomly. If he randomly takes, successively for three time by replacing the book already taken every time, then the mean of the number of mathematics books which is treated as random variable is