Probability is defined as the likelihood of the occurrence of an event. The random experiments are the observations. For example, if we toss a coin, the outcome may be either head or tail. Random experiment is a process where we cannot predict the result of the process. On this page, we have provided detailed information about the random experiments in probability with examples.

## Random Experiment in Probability

An activity that gives an outcome or result is called an experiment. It is an element of uncertainty to which one of these occurs when we perform an experiment or activity. We can get a different number of outcomes from an experiment. If an experiment satisfies these conditions, then it is called a random experiment.

- It is not possible to predict the outcome in advance.
- It has more than one possible outcome.

The below-described terms are used to describe whether an experiment is random or not.

Terms | Meaning |
---|---|

Outcome | The possible result of a random experiment is an outcome. Example: In an experiment of tossing a coin, the outcomes are head or tail. |

Sample space | The set of all possible outcomes of a random experiment is the sample space connected with that experiment and is denoted by S. Example: In an experiment of tossing a coin, sample space S = {H, T} |

Sample point | Every element of the sample space is a sample point. |

### What are Random Experiments?

A random experiment is a process in which the outcome cannot be predicted with certainty in probability. So, a random experiment is an experiment whose outcome cannot be predicted in advance, although all possible outcomes of the experiment are known.

An event E of an experiment is the collection of outcomes. When a dice is thrown, the possible outcomes = 6, those are 1, 2, 3, 4, 5, 6. Therefore, an event is a part of the possible outcome. When the random experiment has a finite number of equally likely outcomes, then the probability of an event E is P(E) = \(\frac { n(E) }{ n(s) } \). Where n(S) is the number of possible outcomes, n(E) is the number of outcomes favourable to an event.

### Examples of Random Experiment

Following are the examples of random experiments and corresponding sample space.

- Tossing a coin three-time
- Number of possible outcomes = 8
- Sample space = S = {HHH, HHT, HTH, THH, TTH, HTT, THT, TTT}

- Throwing a dice
- Number of possible outcomes = 6
- Sample space = S = {1, 2, 3, 4, 5, 6}

- Throwing a dice two times
- Number of possible outcomes = 36
- Sample space = S {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 6), (2, 5), (2, 4), (2, 3), (2, 2), (2, 1), (3, 6), (3, 5), (3, 4), (3, 3), (3, 2), (3, 1), (4, 6), (4, 5), (4, 4), (4, 3), (4, 2), (4, 1), (5, 6), (5, 5), (5, 4), (5, 3), (5, 2), (5, 1), (6, 6), (6, 5), (6, 4), (6, 3), (6, 2), (6, 1)}

### Solved Questions on Random Experiments

**Question 1:**

There are 25 seats numbered from 1 to 25 in a row in a cinema hall. If a seat is selected at random from the row, find the probability that the seat number is

a) A multiple of 5

b) A prime number

**Solution:**

The possible outcomes consist of 25 numbers which are from 1 to 25.

a) The seat number should be a multiple of 5 if it is 5, 10, 15, 20, or 25.

Thus there are 5 multiples of 5 from 1 to 25.

Therefore, the number of favorable outcomes = 5

Probability P(the seat number is a multiple of 5) = \(\frac { 5 }{ 25 } \) = \(\frac { 1 }{ 5 } \)

b) The prime numbers between 1 and 25 are 2, 3, 5, 7, 11, 17, 19, 23.

Thus, there are 9 prime numbers in between 1 and 25.

Probability, P(a seat number is a prime number) = \(\frac { 9 }{ 25 } \)

**Question 2:**

A card is drawn randomly from a deck of 52 playing cards. The pack contains 4 suits, and each suit has 13 cards. Find the probability that the card drawn is

a) Red

b) A diamond

c) A picture card

**Solution:**

There are 13 cards from each suit are they are ACe, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack Queen, and King.

a) Total red cards in a pack of cards = 26 (13 hearts and 13 diamonds)

P(Red) = \(\frac { 26 }{ 52 } \) = \(\frac { 1 }{ 2 } \)

b) There are 13 diamond cards in a pack of cards

P(A diamond card) = \(\frac { 13 }{ 52 } \) = \(\frac { 1 }{ 4 } \)

c) The picture card contains 4 kings, 4 queens nad 4 jacks

Total number of picture cards = 4 + 4 + 4 = 12

P(A picture card) = \(\frac { 12 }{ 52 } \) = \(\frac { 3 }{ 13 } \)

### Frequently Asked Question’s on Random Experiments

**1. Define probability?**

The branch of mathematics that studies a likelihood or a chance of a phenomenon to occur is called probability.

**2. What is meant by random experiments?**

A random experiment is a process in which the outcome cannot be predicted with certainity in probability.

**3. What are examples of random experiment?**

The examples of random experiment are tossing a coin, rolling a die, drawing a ball random from a bag containing red, green and white balls and so on.

**4. What is a random error?**

Random or systematic errors account for all experimental uncertainity. These are stochastic fluctuations in measured data caused by the measuring device accuracy limitations.