$A$ number $n$ is chosen at random from the natural numbers $2$ to $1001$. The probability that $n$ is a number that leaves remainder $1$ when divided by $7$ is:

$A$ coin is tossed. If it shows head,we draw a ball from a bag consisting of $3$ blue and $4$ white balls; if it shows tail,we throw a die. Describe the sample space of this experiment.

$A$ number $x$ is chosen at random from the set $\{1, 2, 3, 4, ......, 100\}$. Then the probability of the event that the chosen number $x$ satisfies the inequality $\frac{(x - 10)(x - 50)}{(x - 30)} \geqslant 0$ is:

$A$ single letter is selected at random from the word $PROBABILITY$. The probability that the selected letter is a vowel is

Two dice are thrown. The events $A, B$ and $C$ are as follows:
$A:$ getting an even number on the first die.
$B:$ getting an odd number on the first die.
$C:$ getting the sum of the numbers on the dice $\leq 5$.
State whether the following statement is true or false and provide a reason:
Statement: $A = B^{\prime}$

$A$ man and his wife appear in an interview for two vacancies. The probability of the husband's selection is $1/7$ and the probability of the wife's selection is $1/5$. What is the probability that only one of them is selected?