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Probability refers to the probability of a specific event occurring. A probability has a number between 0 and 1, indicating that if an event is impossible, the probability is 0 and if it is certain, the probability is 1. Experimental probability is defined as the probability calculated from the findings of an experiment. Empirical probability is another name for this.
Experimental Probability
A probability calculated by a series of tests is known as experimental probability. To assess their possibility, a random experiment is carried out and repeated numerous times, with each repetition referred to as a trial. The experiment is carried out to determine the probability of an event occurring or not occurring. Tossing a coin, rolling a die, or spinning a spinner are all examples. The probability of an event is equal to the total number of trials multiplied by the number of times it has occurred. For example, suppose you flip a coin 30 times and keep track of whether you receive heads or tails. The experimental probability of getting a head is determined as a percentage of the total number of tosses and the number of recorded heads. P(head) = Number of heads recorded in the first 30 tosses.
Experimental Probability Formula
The experimental probability of an event is determined by the number of times the event occurred during the experiment as well as the total number of times the experiment was carried out. Each possible outcome is unknown, and the sample space is the collection of all possible possibilities. P(E) = Number of times an event occurs/Total number of times the experiment is conducted is the formula for calculating the experimental probability.
Theoretical Probability
Theoretical probability is a method of calculating the probability of a certain event’s outcome in probability theory. Probability theory is an area of mathematics concerned with determining the chance of a random event occurring. The probability of an event occurring ranges from 0 to 1. If the probability is near to zero, it means the occurrence is less likely to occur. Similarly, if the probability is closer to 1, it indicates that the event is more likely to occur.
The number of favourable outcomes divided by the entire number of alternative outcomes is theoretical probability. There is no need to do an experiment to ascertain the theoretical probability. However, understanding the context is necessary to determine the probability of that event occurring. Theoretical probability estimates the probability of an event occurring based on the assumption that all occurrences are equally likely to occur.
Experimental Probability VS Theoretical Probability
Experimental outcomes are unpredictable, and they may or may not correspond to theoretical outcomes. Experimental probability results are only near theoretical when the number of trials is greater. Let us examine the distinction between experimental and theoretical probability.
- Exponential Probability: It is based on data acquired following the completion of an experiment. The total number of trials is multiplied by the number of occurrences of an event.
Example: Twenty times a coin is tossed. Heads appeared 12 times and tails appeared 8 times, according to the data.
P(heads)= 12/20= 3/5
P(tails) = 8/20 = 2/5
- Theoretical Probability: Without actually conducting the experiment, this is predicated on what is expected to happen. It is the sum of the following factors: the number of good outcomes; the total number of possible outcomes.
Example: There is a coin toss.
P(heads) = 1/2
P(tails) =1/2
Example Of Experimental Example
Here are some real-life scenarios as examples.
- Patrick made 4, 7, 6, 9, 5, 9, 5 cookies per day during this week.
What is a reasonable estimate of the probability that Patrick will create less than 6 cookies the next day based on this information?
P(6 cookies) =3/7 = 0.428 = 42 %
- The following table displays the number of messages Mike has recently received from six of his pals. 4, 3, 2, 1, 6, 8. Determine the probability that Mike will receive less than two texts the next time.
Solution: Mike has received less than two messages from only two of his six buddies.
As a result, P(2) = 2/6 = 1/3.
Important Note on Experimental Probability
- All of the outcomes’ experimental probabilities add up to 1.
- An event’s probability ranges from 0 to 1, with 0 denoting an impossible event and 1 denoting a certain event.
- Probability can be stated as a percentage as well.
Conclusion
- Without doing an experiment, the theoretical probability is used to calculate the chance of an event occurring.
- Theoretical probability holds that all occurrences have the same chance of happening.
- All of the outcomes’ experimental probability adds up to 1
- An event’s probability ranges from 0 to 1, with 0 being an impossible occurrence and 1 denoting a certain event.
