Random Experiments

Probability theory itself is based on random experiments. Although the outcomes are unpredictable, random experiments are often repeated several times under the same conditions. A random experiment is part of the probability theory and the conditions to be fulfilled are:

Random experiments should be repeated several times under the same conditions

The outcome cannot be predicted in a random experiment.
 

Probability is a mathematical concept used to predict the likelihood of an event. It is calculated by comparing the number of ways an event can occur to the total number of possible outcomes. Follow the given steps to find the probability of random experiments.

Step 1: Identifying the Sample Space
The sample space is the possible outcomes of an experiment.

Step 2: Identify the Favorable Outcomes
Favorable outcomes are the outcomes that satisfy the event for which you want to calculate the probability.

Step 3: Use the Probability Formula

\({\text {Probability }}= {{{\text {Number of Favorable Outcomes }}\over {\text {Total Number of Possible Outcomes }}}}\)

For example, what is the probability of getting exactly two heads when a coin is tossed twice?

When tossing a coin, the possible outcomes are heads or tails.

The possible outcomes when tossing a coin twice are: {HH, HT, TH, TT}

So, the total number of outcomes is 4. 

Here, the favorable outcome is HH

So, the number of favorable outcomes = 1

So, the probability of getting exactly two heads is \(1\over 4\), or 0.25.

When learning probability, it is important to know and understand the terms related to random experiments. The terms used in a random experiment are outcome, sample space, and sample point. 

Understanding random experiments becomes easier when you break down the concepts into simple steps, practice regularly, and observe real-life situations where randomness occurs. Here are helpful tips for students to understand the idea of random experiments. 

• Understand the basics first: Learn key terms such as outcome, sample space, event, and trial before solving problems.
   
• Encourage step-by-step thinking: Teachers can first teach sample space, then favorable outcomes, and finally probability, to help students understand the concept.
   
• Encourage logical thinking: Parents can ask children to guess outcomes and explain why.
   
• Check your sample space: List all possible outcomes to avoid probability errors.
   
• Practice with simple examples: Start with coins, dice, and cards, then move to complex scenarios.

In various fields in our daily lives, we use random experiments. Now, let’s learn some applications of random experiments. 

• In finance, for the stock market analysis and in forecasting the asset price, we use random experiments. 
  
   
• For quality control in manufacturing industries, we use random experiments.
  
   
• When designing games and simulation where the outcomes are determined by random processes like rolling dice or drawing cards.