Random Experiments

Introduction

In our daily lives, each of us engages in a variety of activities, sometimes performing the same activities but also always getting the same consequences.

Here are some examples to understand Random experiments –

• In a math experiment, for example, we frequently say that the sum of all interior angles of a certain quadrilateral is 360 degrees. We don’t know the quadrilateral type or each interior angle
• Moreover, we may undertake a number of scientific tests, the findings of which might not be the same despite the fact that they have been repeated multiple times under uniform conditions
• For example, a coin thrown in the air may land on the head or tail, but we have no way of knowing.

Probability Experiments at Random

An experiment is any action that produces an effect or a result. When doing an experiment or an activity, there is uncertainty about which one could occur. Experiments generally yield a variety of results. In any case, a random experiment is one that meets the two characteristics listed below.

• When there is greater than one probable conclusion from an experiment.
• When it is impossible to foresee the result ahead of time.

Here are some of terms used in the random experiments often used in probability theory. These phrases are used to depict whether an activity is random or not.

 Terms

• Outcome: An outcome is a conceivable result that might be achieved as a consequence of a random experiment. For instance, the probability of a Tuesday in a week would be 1/7.
• Sample space: The set of every possible outcome obtained from a random experiment is known as sample space that is connected with such an experiment. It is represented by the S symbol. For instance, in getting a day in the week, S(Sample Space) = ❴Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday ❵

• Sample point: Every element from the Sample space S is known as a sample point, or every outcome obtained from random experiments is also known as a sample point.

What are Random Experiments?

Using the notion of a random experiment as a guideline,  We can tell whether or not the experiment is random by looking at the results. To help you grasp what is meant by “random experiment” and what is not meant by “random experiment,” we’ve included some concrete examples.

Example 1:

Is it OK to choose a card from a properly shuffled deck of cards as a purely random experiment?

Solution:

As we all know, a deck of cards comprises a total of 52 cards. Each of these cards contains an equal possibility of getting selected.

• The results of this experiment may be repeated indefinitely since we can shuffle the deck several times before picking a card, and as a result, there are a total of 5 potential results.
• Given that it is totally possible to choose any card from the deck of 52 cards, it is impossible to foresee the result beforehand.
• The experiment satisfies both conditions of being a random experiment.
• As a result, it is a completely random experiment.

Example 2:

Take, for example, the experiment of dividing 30 by 5 with the help of a calculator. Check to see whether it was chosen at random or not.

Solution:

• This experiment can be repeated many times under the same conditions, and it will always have the same possible result.
• The result of such an experiment is always 6, which suggests that we can anticipate the outcome of the experiment every time it is repeated.
• Thus, the given experiment is not a random one.

Examples of Random Experimentation

Some instances of random experiments and sample space are shown below.

The act of tossing a coin twice

The number of conceivable outcomes = 4

Example of a space = S = {HH, HT, TH, TT}

Choosing one of the factors of 180

Number of possible outcomes = 18

Sample space = S = {1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180}

Three coins are hurled in a row at the same time.

The number of conceivable outcomes. = 8

Sample space = S = {HHT, HHH,TTT, HTH, TTH,THH, THT, HTT}

Rolling a pair of dice simultaneously

The number of conceivable outcomes = 36

Sample space = S = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}

Throwing a die two times

Number of possible outcomes = 36

Sample space = S = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}

Selecting a card from a urn containing 50 cards numbering from 1 to 50

Number of possible outcomes = 50

Sample space = S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10,….., 45,46,47,48,49,50}

Conclusion

To be concluded from the above-explained details about the random experiments there are many moments in our day-to-day life where we have to take a risk or chance to predict an event easily. We studied about the random experiments using examples in this article which specifies the random experiments more easily.