Three of the six vertices of a regular hexagon are chosen at random. The probability that the triangle with these three vertices is equilateral, is equal to
$\frac{1}{2}$
$\frac{1}{5}$
$\frac{1}{{10}}$
$\frac{1}{{20}}$
Twenty persons arrive in a town having $3$ hotels $x, y$ and $z$. If each person randomly chooses one of these hotels, then what is the probability that atleast $2$ of them goes in hotel $x$, atleast $1$ in hotel $y$ and atleast $1$ in hotel $z$ ? (each hotel has capacity for more than $20$ guests)
In a box, there are $20$ cards, out of which $10$ are lebelled as $\mathrm{A}$ and the remaining $10$ are labelled as $B$. Cards are drawn at random, one after the other and with replacement, till a second $A-$card is obtained. The probability that the second $A-$card appears before the third $B-$card is
If an unbiased die, marked with $-2,-1,0,1,2,3$ on its faces, is through five times, then the probability that the product of the outcomes is positive, is :
If a committee of $3$ is to be chosen from a group of $38$ people of which you are a member. What is the probability that you will be on the committee
If $4 \,-$ digit numbers greater than $5,000$ are randomly formed from the digits $0,\,1,\,3,\,5,$ and $7,$ what is the probability of forming a number divisible by $5$ when, the digits are repeated ?