Experimental Probability - Definition And Examples

Assume that a train is two hours late due to heavy weather, and that the train is scheduled to arrive at the station at 5:00 p.m. You are anticipating the arrival of the train at 5:05 p.m., which is an uncertain event. We can state the probability is less than or equal to one. The probability is the expectancy in this case.

The probability ranges from 0 to 1, with 0 indicating an impossible event and 1 indicating a certain event. It is the observational probability, also known as the empirical probability when the Experimental probability definition is described in experiments (or the relative frequency of events).

Theoretical And Experimental Probability

Theoretical probability assumes that everything will turn out perfectly. Assume you examined the weather for the past five days, beginning today. Today's forecast predicts rain for half of the day and clear skies for the rest. In the next four days, the same will be seen. If I predict that today would be 50% clear and 50% rainy, and assuming the best-case scenario, 70% of the next day will be clear and 30% will be rainy.

So, you simply made a hypothesis of the circumstance, which means you, when you assumed the rest to be exactly 50-50. The experimental probability was 70-30 when the result was 70-30. Because the experimental probability meaning is based on experiments, practical effort, or fieldwork rather than leading daydreaming assumptions, as you did in the example of the train's estimated arrival time.

As a result, the experimental probability gives you the precise outcome of an experiment, which may differ from the theoretical likelihood.

What Is Experimental Probability?

Experimental probability is a type of probability that is based primarily on a set of tests.

To evaluate their likelihood, a random experiment is conducted and repeated numerous times, with each repetition serving as a trial.

Because the experiment is being undertaken to determine whether or not an event will occur, i.e., the probability of an event occurring. Tossing a coin, throwing dice, or whirling a spinner are all examples. The probability of an event is always equal to the number of times it occurs divided by the total number of trials in mathematics.

Assume you flip a coin 50 times and keep track of whether you get a "head" or "tail." The experimental probability of getting a "tail" is computed as a percentage of the number of heads and total tosses, i.e.,

P (tail) = Number of tails recorded ÷  50 tosses

Where, P stands for the probability of an event occurring.

What does Experimental Probability Talk About?

The experimental probability describes the experiment's actual outcome. Let's imagine you run a 100-fold coin flip experiment. The coin has a theoretical probability of 50 percent heads and 50 percent tails.

In reality, the results of your experiment show 47 heads and 53 tails. This suggests that the experimental likelihood of receiving tails in 100 flips is 53 percent, whereas the experimental probability of getting heads in 100 trials is 47 percent. So, the 50-50 and 53-47 results, respectively, refer to theoretical and experimental probability.

Experimental Probability Formula

The experimental probability of an event occurring is calculated by dividing the number of times the event occurred during the experiment by the total number of times the experiment was conducted.

As a result, each possible outcome is uncertain, and the sample space is the collection of all possible outcomes. The Experimental Probability Formula assists us in calculating the experimental probability, which is calculated as follows:

Assume you spin a spinner 50 times, and the table below reveals the results of your experiment.

Image: 

Spinner

We can now calculate the experimental probabilities of spinning the colour pink using this table.

Because a spinner turns 50 times and the pink colour appears 10 times, the total number of events or times a spinner revolves is 50.

As we know from the probability formula, the P(E) of an event is the number of occurrences divided by the total number of events done.

P (E)  =  10/50  = 1/5

As a result, the probability of the pink colour appearing on spinning is 1/5.

Let's look at some experimental probability examples to better comprehend the notion of experimental probability.

Experimental Probability Examples

1. The number of pancakes prepared by Fredrick per day this week is in the order of 4, 7, 6, 9, 5, 9, and 5. What will you say if I ask you to give me a credible estimate of the likelihood that Fredrick will make less than 6 pancakes the next day based on this data?

Solution:

You say that P(< 6 pancakes) = 4, 5, 5 =  3 possibilities 

Mathematically, we get: 3/7 = 0.428 = 42%

As a result, there's a 42 percent chance that Fredrick will make less than six pancakes the next day.

2. Now you must calculate the likelihood that while ordering an exotica pizza, the next order will not include a Schezwan Sauce topping.

The following can be found on an exotica pizza:

Looking at the data table above, we can see that the realistic estimate of the probability that the next type of topping ordered will not be a Schezwan sauce is 27/43 = 62.8 %.

The preceding examples depict a real-life experimental probability scenario.

Experimental Probability Questions

1. The following table shows the observations made after throwing a 6-sided die 80 times:

Find the probability of an experiment in a throw of dice of a) obtaining a four; b) Obtaining a number less than 4, and c) Rolling a 3 or 6

Solution:

We receive the numbers 1, 2, 3, 4, 5, and 6 from a single roll of the dice. Now we'll take each step toward our goals one by one. We know how to calculate the Experimental probability using the formula: The total number of trials divided by the number of times an event happens.

1. Obtaining a score of 4: 14/80=0.175, or 17.5 percent.

2. When you roll a number that is fewer than four, you have a chance of winning. One, two, and three are the outcomes. Each has a frequency of 13, 10, and 15 respectively. Now add them all together to obtain the total number of times an event happened, which is 38. P (numbers less than 4) = 38/80 = 0.475 or 47.5 percent.

3. The same goes for rolling a 3 or 6: 31/80 = 0.387 or 38.7%.

Q2: Which of the following is a probability experiment?

1. 17/11

2. - 0.32

3. 2.4

4. 65%

Answer: Option (d): The value of experimental probability represented as a percentage ranges from 0 to 1.

Practise Question MCQs

1. If the probability of an event happening is 0.3 and the probability of the event not happening is_____

1. 0.7

2. 0.6

3. 0.5

4. None of the above

Ans: A

2. 200 times, three coins were tossed. There were 72 times when two heads appeared.  Then the probability of 2 heads coming up is

1. 1/25

2. 2/25

3. 7/25

4. 9/25

Ans: D

Conclusion

In the nutshell, the experimental probability focuses on the result of an experiment, while the theoretical probability is just an assumption that we make to work on our experiments.