Probability is the branch of mathematics that deals with the possibility of any outcome of an event or experiment. 

There are different types of probabilities. Classical probability states the possible outcome of any event in a classic manner. On the other hand, statistical probability involves the laws governing random events and their data collection, analysis, interpretation, and display.  In other words, we can say that in a classical probability, the possible outcomes are at equal odds. For example, when we roll a dice, there are 50-50% chances of getting an even and odd number. Similarly, when we toss a coin, there are equal chances of getting either a head or a tail. Therefore, we can conclude that classical probability is the simplest and easiest to understand probability type.

Classical Probability

As stated above, the classical probability is the probability of any event in a classic manner, i.e. equal happening of events. When we roll a dice, the probability of each number is equal to 1/6 of the equal. This is an example of a classical probability.

The Formula of Classical Probability

The formula of classical probability is as follows:

P(A)= f/N

Where P(A)= classical probability

f= Frequency or the number of favourable outcomes

N= Number of total possible outcomes.

Examples of Classical Probability in Daily Life

Example 1

Suppose you have a multiple-choice format exam of mathematics tomorrow. There will be four options: A, B, C, and D. You know that any of these options can be correct. Thus, by the formula of probability, we can say that the probability of getting a correct answer in each case is ¼, i.e., 25% for each option.

Example 2

We usually toss a coin while deciding the teams for batting or bowling. The coin has two sides, i.e., a head and a tail. Thus, there are equal chances of getting a head and a tail. Therefore, it is an example of classical probability with 50% chance of each outcome.

Statistical Probability

In statistics, we collect the data in a specific form and represent it in an order to get the result. Similarly, if we talk about statistics in probability, it deals with governing events, collecting data of events, and also its representation in a specific manner for better understanding.

Let’s take an example of a coin. If we toss a coin four times, the outcomes will vary. It can either be 50-50 or all head or all tails or maybe 3 heads-1 tails and vice versa. But by tossing the same coin 400 times, we shall get the heads and tails in approx. equal ratios. We can collect the data and analyse it to calculate the probable outcome of it.

How to Calculate Statistical Probability?

We can calculate statistical probability just like other probability questions. We need the number of favourable outcomes and total outcomes for the calculation. By dividing the number of favourable outcomes by the number of total outcomes, we can get the statistical probability of that event. The statistical probability will also involve representing it in a certain way (like a frequency table or a graph) for better analysis.

Probability(Event) = Favorable Outcomes/Total Outcomes = x/n

Other Types of Probability

There are three other types of probabilities. These are as follows:

Empirical Probability: Empirical probability is the type of experimental probability that evaluates outcomes based on conducting experiments. For instance, if you roll a weighted dice without knowing the side having weight, you’ll get the idea of the probability of each time (outcome) by rolling that dice a number of times and determining the proportion of times the dice gives that desired outcome. That outcome will then be the probability.

Subjective Probability: Subjective probability deals with one’s own belief of the happening or not happening of a certain event. For example, while watching a cricket match, you believe that the probability of winning your favourite team is the highest. However, the fans of the other team might think the opposite. Therefore, subjective probability is completely based on a person’s belief.

Axiomatic Probability: While calculating axiomatic probability, we must follow certain rules or axioms specified by Kolmogorov. By these rules, we determine whether the event will happen or not. These three rules are as follows:

• The first point states that the least possibility or probability of happening an event is 0. Similarly, the highest probability is 1.
• Every certain event (an event that must occur) has the probability 1.
• Two mutually exclusive events will never occur simultaneously. However, we can say that only one of them will happen. For example, any place will either have a hot or cold climate at a time (not both).

Solved Questions on Classical and Statistical Probabilities

1. Nina wants a head to win the toss. What is the possibility of winning for Nina? 

Solution:

Number of total possible outcomes= 2

Number of favourable outcomes= 1

Tossing a coin is an example of classical probability. Therefore, we can use the formula of classical probability:

P(A)= f/N

= ½

2. Aman needs an even number to escape the snake while playing the game of snakes and ladders. What is the probability of winning for Aman?

Solution:

Number of total possible outcomes= 6

Number of favourable outcomes= 3

P(A)= f/N

= 3/6

=1/2

Conclusion 

Classical probability states the possible outcome of any event in a classic manner, whereas statistical probability is the statistical representation of any random even. In classical probability, all the outcomes have equal odds of happening. For example, rolling a dice or tossing a coin. 

The formula of classical probability is as follows: P(A)= f/N; where, P(A)= classical probability, f= frequency or the number of favourable outcomes and N= Number of total possible outcomes. There are three more types of probabilities: empirical, subjective and axiomatic probabilities.