Understanding the probability of an event involves comparing favorable outcomes to total possible outcomes.
When a standard coin is thrown, it has two possible sides: Head (H) and Tail (T).
The question asks for the probability of *not* getting a head. This means the favorable outcome is getting a tail.
The formula for probability is:
$ P(\text{Event}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} $
Applying this to our event (not getting a head, which is getting a tail):
$ P(\text{Not getting Head}) = P(\text{Getting Tail}) = \frac{1}{2} $
Thus, the probability of not getting a head is $\frac{1}{2}$.
Match List - I with List - II. Suppose A, B and C are three non-empty sets.
| List - I | List - II |
| A. De-Morgan's Law | I. $A \setminus B = A \cap B^C$ |
| B. Associative Law | II. $(A \cup B)^C = A^C \cap B^C$ |
| C. Distributive Law | III. $A \cup (B \cap C) = (A \cup B) \cap (A \cup C)$ |
| D. Difference of sets Law | IV. $(A \cup B) \cup C = A \cup (B \cup C)$ |
Choose the correct answer from the options given below :
Match List - I with List - II.
| List - I | List - II |
| A. Domain of function $f(x) = \frac{1}{\sqrt{x^2 - 1}}$ | I. $[2, \infty)$ |
| B. Range of function $f(x) = \frac{1}{\sqrt{x^2 - 1}}$ | II. $(-\infty, -1) \cup (1, \infty)$ |
| C. Domain of function $f(x) = \sqrt{x - 2}$ | III. $(0, \infty)$ |
| D. Range of function $f(x) = \sqrt{x - 2}$ | IV. $[0, \infty)$ |
Choose the correct answer from the options given below :
Match List - I with List - II on the basis of relationship.
| List - I | List - II |
| A. Complement operation | I. all possible subsets |
| B. Power set operation | II. tuples (ordered) |
| C. Cartesian product | III. universal set |
| D. Union and intersection | IV. difference (symmetric) |
Choose the correct answer from the options given below :
Morgenthau's principles of political realism are:
A. Politics is rooted in permanent and unchanging human nature which is basically self centred, self-regarding and self-interested
B. Politics is an autonomous sphere of action and cannot therefore be reduced to morals
C. International Politics is an arena of conflicting self-interests
D. The ethics of international relations is situational ethics which is very different from private morality
Choose the correct answer from the options given below:
Who among the following political thinkers consider the anarchical self help system to be a compelling factor for States to maximise their relative power positions?