In a university campus, the probability that a person chosen at random is an engineering student is $\frac{1}{5}$. The probability of having atmost two engineering students in a sample of 8 people is

When two dice are thrown, the probability of getting an ordered pair $(x, y)$ such that $x^2+y^2 \leq 25$ where $x$ and $y$ are numbers that show up on the two dice, is

If two cards are drawn simultaneously from a well shuffled pack of 52 cards, then the probability of getting a card having a prime number and a card having a number which is a multiple of 5 is

If $A$ and $B$ are two events of a random experiment such that $P(\bar{A})=\frac{2}{3}, P(B)=\frac{4}{15}$ and $P(A \cap \bar{B})=\frac{1}{5}$, then $\sqrt{195[P(B \mid(A \cup \bar{B}))+P(A \cup B)]}=$