What is the probability that the sum of two numbers chosen at random from $40$ consecutive natural numbers is odd?

$A$ bag contains $8$ black and $7$ white balls. Two balls are drawn at random. For which outcome is the probability the highest?

$A$ box contains coupons labelled $1, 2, \ldots, 100$. Five coupons are picked at random one after another without replacement. Let the numbers on the coupons be $x_1, x_2, \ldots, x_5$. What is the probability that $x_1 > x_2 > x_3$ and $x_3 < x_4 < x_5$?

From the first $100$ natural numbers, two numbers $a$ and $b$ are selected randomly without replacement. If the probability that $a-b \ge 10$ is $\frac{m}{n}$, with $\gcd(m, n)=1$, then $m+n$ is equal to:

$A$ committee of $5$ is to be formed from a group of $9$ people. What is the probability that a specific married couple is either both included or both excluded from the committee?

Two integers are drawn at random from the set $\{5, 6, \ldots, 35\}$. What is the probability that their difference is odd?