Experimental Probability
The chance or occurrence of a particular event is termed its probability. The value of a probability lies between 0 and 1 which means if it is an impossible event, the probability is 0 and if it is a certain event, the probability is 1. The probability that is determined on the basis of the results of an experiment is known as experimental probability. This is also known as empirical probability.
What is Experimental Probability?
Experimental probability is a probability that is determined on the basis of a series of experiments. A random experiment is done and is repeated many times to determine their likelihood and each repetition is known as a trial. The experiment is conducted to find the chance of an event to occur or not to occur. It can be tossing a coin, rolling a die, or rotating a spinner. In mathematical terms, the probability of an event is equal to the number of times an event occurred ÷ the total number of trials. For instance, you flip a coin 30 times and record whether you get a head or a tail. The experimental probability of obtaining a head is calculated as a fraction of the number of recorded heads and the total number of tosses. P(head) = Number of heads recorded ÷ 30 tosses.
Experimental Probability Formula
The experimental probability of an event is based on the number of times the event has occurred during the experiment and the total number of times the experiment was conducted. Each possible outcome is uncertain and the set of all the possible outcomes is called the sample space. The formula to calculate the experimental probability is: P(E) = Number of times an event occurs/Total number of times the experiment is conducted
Consider an experiment of rotating a spinner 50 times. The table given below shows the results of the experiment conducted. Let us find the experimental probability of spinning the color - blue.
| Color | Occurrences |
|---|---|
| Pink | 11 |
| Blue | 10 |
| Green | 13 |
| Yellow | 16 |
The experimental probability of spinning the color blue = 10/50 = 1/5 = 0.2 = 20%
Experimental Probability vs Theoretical Probability
Experimental results are unpredictable and may not necessarily match the theoretical results. The results of experimental probability are close to theoretical only if the number of trials is more in number. Let us see the difference between experimental probability and theoretical probability.
| Experimental Probability | Theoretical Probability |
|---|---|
| It is based on the data which is obtained after an experiment is carried out. | This is based on what is expected to happen in an experiment, without actually conducting it. |
| It is the result of: the number of occurrences of an event ÷ the total number of trials | It is the result of: the number of favorable outcomes ÷ the total number of possible outcomes |
|
Example: A coin is tossed 20 times. It is recorded that heads occurred 12 times and tails occurred 8 times. P(heads)= 12/20= 3/5 P(tails) = 8/20 = 2/5 |
Example: A coin is tossed. P(heads) = 1/2 P(tails) =1/2 |
Experimental Probability Examples
Here are a few examples from real-life scenarios.
a) The number of cookies made by Patrick per day in this week is given as 4, 7, 6, 9, 5, 9, 5.
Based on this data, what is the reasonable estimate of the probability that Patrick makes less than 6 cookies the next day?
P(< 6 cookies) = 3/7 = 0.428 = 42%
b) Find the reasonable estimate of the probability that while ordering a pizza, the next order will not be of a pepperoni topping.
| Pizza Toppings | Number of orders |
|---|---|
| Mushrooms | 4 |
| Pepperoni | 5 |
| Cheese | 7 |
| Black Olives | 4 |
Based on this data, the reasonable estimate of the probability that the next type of toppings that would get ordered is not a pepperoni will be 15/20 = 3/4 = 75%
Related Sections
- Card Probability
- Conditional Probability Calculator
- Binomial Probability Calculator
- Probability Rules
- Probability and Statistics
Important Notes
- The sum of the experimental probabilities of all the outcomes is 1.
- The probability of an event lies between 0 and 1, where 0 is an impossible event and 1 denotes a certain event.
- Probability can also be expressed in percentage.
Frequently Asked Questions (FAQs)
How do you Find the Experimental Probability?
The experimental probability of an event is based on actual experiments and the recordings of the events. It is equal to the number of times an event occurred divided by the total number of trials.
What is the Experimental Probability of rolling a 6?
The experimental probability of rolling a 6 is 1/6. A die has 6 faces numbered from 1 to 6. Rolling the die to get any number from 1 to 6 is the same and the probability (of getting a 6) = Number of favorable outcomes/ total possible outcomes = 1/6.
What is the Difference Between Theoretical and Experimental Probability?
Theoretical probability is what is expected to happen and experimental probability is what has actually happened in the experiment.
Do You Simplify Experimental Probability?
Yes, after finding the ratio of the number of times the event occurred to the total number of trials conducted, the fraction which is obtained is simplified.
Which Probability is More Accurate, Theoretical Probability or Experimental Probability?
Theoretical probability is more accurate than experimental probability. The results of experimental probability are close to theoretical only if the number of trials are more in number.