Experimental Probability

Probability, a branch of Math that deals with the probability of occurrence of a given case. The probability values for the experiment are typically specified within the number range. The values are between the numbers 0 and 1. The chance value can not be negative. Basic rules, such as addition, multiplication, and supplementary rules, are linked to the probability.

What is Experimental Probability?

Experimental probability, also known as Empirical probability, is based on real observations and sufficient records of the occurrence of events. A series of actual experiments are conducted to determine the occurrence of any event. Experiments that do not have a predetermined outcome are known as spontaneous experiments.


The outcome of these experiments is uncertain. Random tests are repeated several times to determine their probability. An experiment is repeated a fixed number of times, and every repetition is known as a trial. Mathematically, the experimental probability formula is defined by -


Probability of occurrence P(E) = Number of times an occurrence occurs / Total number of tests.


Have you ever played cards with a deck? If you don't, have you ever rolled a die? Or at least, I 'm sure you've also flipped a coin! All of these can be applied to the concept of experimental probability, which is the ratio of the number of times the outcome occurs to the total number of times the activity is performed. Let's go over this concept by using coins, decks, and dice.


Let us consider one more way -


You and your three friends are playing a board game. It's your turn to roll the die and win the game you need a 5 on the dice. Now, is it true that you're going to get an exact 5 when you roll the die? No, it's a matter of chance. We face multiple situations in real life where we have to take a chance or take a risk.

On the basis of such variables, the probability of occurrence of a certain event can be accurately predicted. During our day-to-day life, we learn all about the terms 'chance and possibility.' So, here’s to understanding experimental probability definition -


In basic terms, the probability of occurrence of a given event is what we are expected to test. In this article, we will discuss in detail one of the types of probability called "Experimental Probability."

Flipping a Coin

If you flip a coin, there are two potential outcomes: the head or the tail. If you flip a coin 100 times, at least theoretically, it is possible that the heads will appear 50 times or half the time. In other words, our theoretical chance of turning our heads is 1⁄2 or 50 percent. However, this may not be the case in reality, in a particular experiment focused on research and observation.


Here's what I actually meant. Take the coin out for me. I'm going to wait. Okay, flip the coin 10 times, and pull down the number of times you 're going to get your heads in this experiment. I did the experiment, and I had my heads 7 out of 10 times. What is the experimental probability, in my case, that a coin flip will yield heads? 7 out of 10, or 70% of the time. Maybe my coin isn't fair, or maybe it's just a chance that created this result on its own. However, if we were to turn a rational coin a thousand times, the experimental odds would be closer to matching the theoretical odds.

 

Example: You asked your 3 friends Shakshi, Shreya and Ravi to toss a fair coin 15 times each in a row and the outcome of this experiment is given as below:

Probability Experimental Example 

Coin Tossed By:

No. of. Heads

No. of. Tails

Shakshi

6

9

Shreya

7

8

Ravi

8

7

Solution: The experimental probability of the occurrence of heads and tails in this experiment can be calculated as - 

Experimental probability of the occurrence of the head = Number of times the head occurs / The number of times the coin is tossed. 

Experimental probability of occurrence of tails = number of times the tails occur / number of times the coin is tossed.

Calculate the Probability of Occurrence of Heads and Tails.

Coin Tossed By:

No. of. Heads

No. of. Tails

Experimental Probability for the occurrence of Head

Experimental Probability for the occurrence of Tail

Shakshi

6

9

6/15 = 0.4

9/15 = 0.6

Shreya

7

8

7/15 = 0.47

8/15 = 0.53

Ravi

8

7

8/15 = 0.53

7/15 = 0.47

 

We observe that if the number of tosses of the coin increases then the probability of occurrence of heads or tails also approaches 0.5.

FAQ (Frequently Asked Questions)

1. What is experimental probability? How are you going to calculate the experimental likelihood of an event?

Experimental probability refers to the probability that an occurrence happens after an experiment has been performed. 


For such a scenario, the likelihood of an occurrence is determined by an actual experiment. Mathematically speaking, Experimental probability formula - 

Experimental probability = Number of event occurrences / Total number of trials


For example, if the dice are rolled 6000 times and the number '5' is rolled 990 times, then the experimental probability that '5' appears on the dice is 990/6000 = 0.165.


Step 1 - Conduct an experiment and record the number of times the event occurs and the number of times the activity takes place. 

Step 2 - Divide the two numbers in order to obtain the experimental probability


2. What do you mean by Theoretical probability?

The theoretical probability is determined by theoretically considering all potential outcomes and by evaluating how likely the outcome is. Mathematically speaking, 


Theoretical probability = Number of favorable outcomes / Total number of outcomes


For example, the theoretical probability that the number '5' appears on the dice when rolled is 1/6 = 0.167. This is because of the 6 possible outcomes (in dice showing '1,' '2,' '3,' '4,' '5,' '6'), only 1 outcome (in dice showing '5') is favorable.