# Experimental Probability

At first we

will know the precise meaning of the term ‘experiment’ and the proper context

in which it will be used in our experimental probability.

**Definition of experiment:** A process which can produce some well-defined results (outcomes) is called an experiment.

Some Experiments and their outcomes:

**I. Tossing a coin: **

Suppose we toss a coin and let it fall flat on the ground. Its upper face will show either Head (H) or Tail (T).

1. Whatever comes up, is called an outcome.

2. All possible outcomes are Head (H) and Tail (T).

**II.
Throwing a dice: **

A dice is a solid cube having 6 faces, marked as 1, 2, 3, 4, 5, 6 respectively.

Suppose we throw a dice and let it fall flat on the ground. Its upper face will

show one of the numbers 1, 2, 3, 4, 5, 6.

- Whatever comes up, is called

an outcome. - All possible outcomes are 1,

2, 3, 4, 5, 6.

The act of

tossing a coin or throwing a dice is called an experiment.

Whatever comes up, is called an outcome.

In an experiment, all possible outcomes are known.

The plural

of die is dice.

**III.
Drawing a card from a well-shuffled deck of 52 cards: **

A deck of

playing cards has in all **52** cards.

1. It has 13

cards each of four suits, namely ** spades**,

**,**

*clubs***and**

heartshearts

**.**

*diamonds*

- Cards of spades and clubs

are**black**cards. - Cards of hearts and diamonds

are**red**cards.

2. Kings,

queens and jacks (or knaves) are known as face cards. Thus, there are 12 face

cards in all.

**Definition
of Experimental Probability:** The experimental probability of happening of an event

is the ratio of the number of trials in which the event happened to the total

number of trials.

The

experimental probability of the occurrence of an event E is defined as:

Number of trials in which event happened

^{P(E) = }

Total number of trials

Solved examples on Experimental Probability:

**1.** Suppose we toss a coin 100 times and get a head 58 times. Now, we toss a coin at random. What is the probability of getting a head?

**Solution:**

Total number of trials = 100.

Number of times head appeared = 58.

*Number of times head appeared
^{ Probability of getting a head = }
Total number of trials *

= ^{58}/_{100}

= ^{29}/_{50}

**2. A coin is tossed 150 times and head is obtained 71 times. Now, if a coin is tossed at random, what is the probability of getting a tail?**

**Solution:
**

**Total number of trials = 150.
Number of times head appeared = 71.
**Number of times tail appeared = (150 – 71) = 79.

*Number of times tail appeared
^{ Probability of getting a tail = }
Total number of trials *

= ^{79}/_{150}