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.

1. Whatever comes up, is called
   an outcome.
2. 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,
hearts and 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