Introduction
The meaning of probability in a dictionary is “how likely something is to happen “or “something likely to happen .” In more general terms, probability is the study of things that might happen. We use it all the time, typically without even thinking about it. We do not solve genuine probability issues in our daily lives but rather utilise subjective probability to choose the course of action or any conclusion. Everything from weather predictions to the possibility of dying in an accident is a probable event.
In real life also probability is utilised to predict some situations like the example given below:
Weather Forecasting: We always check the weather forecast before going on a trip or having a picnic. Assume the forecast indicates an 80% likelihood of rain. Do you ever wonder where the other 80% comes from? Meteorologists forecast the weather using a particular instrument and approach. They examine the previous days’ historical databases, which have a comparable temperature, humidity, pressure characteristics, etc. And figure out that it rained 80 times out of 100 on similar days in the past.
Source: Siyavula
In mathematics, it is the capacity to comprehend and evaluate the possibility of any given set of occurrences. The probability is a number between 0 and 1 that represents how likely something is going to happen.
The number of possible outcomes in the sample space divided by the number of possible outcomes defines the probability of an occurrence. The collection of all potential outcomes of an event is referred to as the sample space of that event.
P(E) = n(E)/n(S)
If P(E) represents the probability of an event E, then:
 P(E) = 0 if and only if E is an impossible event.
 P(E) = 1 if and only if E is a certain (or sure) event.
 0 ≤ P(E) ≤ 1.
For examples:
 You made a coin toss. It's either head or tail for your sample space.
The probability of arriving HEAD is:
P(H) = 1/2 = 0.5, i.e., ( 0 <= 0.5 <= 1)
 You roll the dice. 1,2,3,4,5,6 is your sample space.
The probability of arriving 6 is:
P(6) = 1/6 = 0.16666667, i.e., ( 0 <= 0.166666 <= 1)

Impossible event The event that cannot occur at any chance is known as the Impossible event. An impossible event has a probability of 0 since it cannot happen in any circumstance.
For example:
Getting a 7 on a dice is an improbable occurrence with a 0% chance of occurring. (Because dice contains numbers from 1 to 6) 
Sure event: A sure occurrence is predetermined to occur.
For example:
Tossing a coin once and getting a head or tail is a foregone conclusion since the outcome will always be head or tail. As a result, the chance of a certain thing happening is one.
Now that you have a basic understanding of what exactly probability is, let's solve some examples to grasp the concept in a better way
Questions based on coins
Source: Tenor
Example 1: A coin is tossed two times. What are the chances of getting at least one head?
Solution:
For any question, the strategy should be to locate the sample spaces first. The coin is tossed twice in this game, with the first time having a chance of landing on either HEAD or TAIL (2). The same is true for the second turn, which is Head or Tail (2).
As a result, the total sample spaces are 2+2 = 4 (HH, HT, TH, TT).
The formula is P(E) = n(E)/n(S), where n(S) = 4.
Using the above sample spaces, n(E) can be computed. We must calculate the chance of receiving at least one head, which implies one or more HEAD.
Now, n(E) = 3 and n(S) = 4
P(E) = n(E)/n(S)
= ¾
= 0.75
Practice Question: A coin is thrown 3 times. What is the probability that at least one head is obtained? ( Ans = 0.875)
Example 2: A coin is tossed three times. What is the probability of getting 2 Heads and 1 Tail if the probability of a head is 0.4 and the tail is 0.6?
Solution:
List of the possible outcomes = {HHH,HHT,HTH,THH,TTH,THT,HTT,TTT}
Now, count the number of times the event is matching with our expectations:
Count = 3
As we are given the probability in the question itself hence, we will go accordingly. Such types of problems are known as Biased problems.
HxHxT + HxTxH + TxHxH = (0.4 x 0.4 x 0.6) + (0.4 x 0.6 x 0.4) + (0.6 x 0.4 x 0.4)
= 0.288
Practice Question: Assume we have a biased coin with a 2/3 chance of coming up heads. This coin will be flipped three times. What is the chance that it lands on heads twice in a row? (Ans = 4/9 )