Experimental Probability Example

Example: Suppose you roll a six-sided die 100 times, and you observe that the number 4 comes up 18 times.

Solution:

Experimental probability of rolling a 4 is:

Number of Times Event Occurs (rolling a 4): 18

Total Number of Trials (total rolls): 100

Experimental Probability = (Number of Times Eevent Occurs) / (Total Number of Trials)

= 18 / 100 = 0.18

So, the experimental probability of rolling a 4 on a six-sided die in this experiment is 0.18.

Theoretical Probability

Theoretical Probability calculates the likelihood of an event based on known outcomes, assuming equal likelihood. It’s fundamental in predicting probabilities without relying on experimental data.

In this article, we will learn about, theoretical probability, and experimental probability, their differences, examples, applications, and others in detail.

Table of Content

  • What is Probability?
  • What is Theoretical Probability?
    • Formula for Theoretical Probability
  • How to Find Theoretical Probability?
  • Examples on Theoretical Probability
  • Experimental Probability Definition
  • Experimental Probability Example
  • Theoretical Probability Vs Experimental Probability

Similar Reads

What is Probability?

Probability is the measure of the chance that an event will happen; it is a number between 0 and 1. An event is certain to happen if its probability is one, and zero if it is impossible. In flipping a coin, for example, the chance it will land heads is 0.5. This is so because heads are one of the two possible results. Either by seeing and closely examining facts or by understanding every imaginable scenario, probability may be computed....

What is Theoretical Probability?

An event’s chance of happening is measured theoretically using known probable outcomes. It is computed by dividing the number of favourable results by all feasible outcomes. With this approach, any result is assumed to be equally probable. On a fair six-sided die, for instance, the theoretical chance of rolling a 3 is 1/6 since there is only one favourable result—rolling a 3—and six potential outcomes—rolling any number from 1 to 6....

How to Find Theoretical Probability?

Clearly define the experiment or random process you are thinking about. Determine the Sample Space by making a list of every experiment result....

Examples on Theoretical Probability

Various examples on Theoretical Probability are added below:...

Experimental Probability Definition

Experimental probability is the chance of a happening given the real outcomes of a trial or experiment. It is computed by dividing the overall number of trials carried out by the frequency of the occurrence....

Experimental Probability Example

Example: Suppose you roll a six-sided die 100 times, and you observe that the number 4 comes up 18 times....

Theoretical Probability Vs Experimental Probability

Aspect Theoretical Probability Experimental Probability Definition Based on the expected likelihood of events occurring Based on the actual results from experiments or trials Calculation Method Number of favourable outcomes divided by total possible outcomes Number of successful outcomes divided by total trials Basis Assumes all outcomes are equally likely Relies on empirical data gathered from experiments Example Probability of rolling a 3 on a fair six-sided die is 1/6 Probability calculated after rolling a die 100 times Reliability Idealized, assumes perfect conditions Reflects real-world variability and experimental error Use Case Used in theoretical models, predictions, and simulations Used to verify theoretical models and in practical applications Dependence on Data No need for actual data, purely based on possible outcomes Requires collection of data from repeated experiments Variability Fixed value for a given scenario Can vary depending on the experimental conditions...

Conclusion

In conclusion, theoretical probability is based on expected outcomes under ideal conditions, while experimental probability is derived from actual experimental results. Both methods are essential in different contexts: theoretical probability for predictions and models, and experimental probability for real-world applications and validation....

FAQs on Experimental Probability

What is Theoretical Probability?...