An electronic assembly consists of two subsystems,$A$ and $B$. From previous testing procedures,the following probabilities are known:
$P(A \text{ fails}) = 0.2$
$P(B \text{ fails alone}) = 0.15$
$P(A \text{ and } B \text{ fail}) = 0.15$
Evaluate the probability $P(A \text{ fails alone})$.

Let $X$ be the set consisting of the first $2018$ terms of the arithmetic progression $1, 6, 11, \dots$ and $Y$ be the set consisting of the first $2018$ terms of the arithmetic progression $9, 16, 23, \dots$. Then,the number of elements in the set $X \cup Y$ is:

In a college of $300$ students,every student reads $5$ newspapers and every newspaper is read by $60$ students. The number of newspapers is

Let $A$ denote the set of all $2$-digit numbers in base $10$ that are equal to four times the sum of the factorials of their digits. The sum of the numbers in $A$ is

Out of $60 \%$ female and $40 \%$ male candidates appearing in an exam,$60 \%$ of the total candidates qualify it. The number of females qualifying the exam is twice the number of males qualifying it. $A$ candidate is randomly chosen from the qualified candidates. The probability that the chosen candidate is a female is:

Let $A = \{x : |x^{2} - 10| \le 6\}$ and $B = \{x : |x - 2| > 1\}$. Then: