Three randomly chosen nonnegative integers $x, y$ and $z$ are found to satisfy the equation $x+y+z=10$. Then the probability that $z$ is even, is

A bag contains $8$ black and $7$ white balls. Two balls are drawn at random. Then for which the probability is more

A bag contains six balls of different colours. Two balls are drawn in succession with replacement. The probability that both the balls are of the same colour is p. Next four balls are drawn in succession with replacement and the probability that exactly three balls are of the same colours is $q$. If $p : q = m$ $: n$, where $m$ and $n$ are coprime, then $m + n$ is equal to $..........$.

Out of $100$ students, two sections of $40$ and $60$ are formed. If you and your friend are among the $100$ students, what is the probability that you both enter the same section ?

Out of $40$ consecutive natural numbers, two are chosen at random. Probability that the sum of the numbers is odd, is

A card is drawn at random from a pack of $100$ cards numbered $1$ to $100$. The probability of drawing a number which is a square is