Introduction
Probability is used in such situations where outcomes of an event is not certain.
For Example :
(1) It will probably rain today.
(2) I doubt that he will pass the test.
(3) Most probably, Kavita will stand first in the annual examination.
(4) Chances are high that the prices of diesel will go up.
(5) There is a 50-50 chance of India winning a toss in today’s match.
The words ‘probably’, ‘doubt’, ‘most probably’, ‘chances’, etc., used in the statements above involve an element of uncertainty.
❝The uncertainty of ‘probably’ etc can be measured numerically by means of ‘probability’ in many cases.❞
We can get a glimpse of probability when we performed experiments like tossing of coins, throwing of dice, etc., by observe their outcomes.
Define :
Experimental / Empirical Probability
The experimental or empirical probability P(E) of an event E is defined as
The empirical interpretation of probability can be applied to every event associated with an experiment which can be repeated a large number of times. The requirement of repeating an experiment has some limitations, as it may be very expensive or unfeasible in many situations. This is why for all such situations we use theoretical probability
Theoretical / Classical Probability
The theoretical probability (also called classical probability) of an event E, written as P(E), is defined as
Here, we assume that the outcomes of the experiment are equally likely. This definition of probability was given by Pierre Simon Laplace in 1795.
From the definition of the probability P(E), we see that the numerator (number of outcomes favourable to the event E) is always less than or equal to the denominator (the number of all possible outcomes). Therefore,
0 ≤ P(E) ≤ 1
The probability of an event which is impossible to occur is 0. Such an event is called an impossible event while the probability of an event which is sure (or certain) to occur is 1. Such an event is called a sure event or a certain event.
Examples of Probability from Daily Life
In the beginning, the probability started with gambling but today it has been used extensively in the fields of Physical Sciences, Commerce, Biological Sciences, Medical Sciences, Weather Forecasting, etc.
Most Common Uses
1) Weather Forecasting
2) Medical Decisions
3) Politics
4) Sports (Cricket, Football Match)
5) Typing on a Smart Device
6) Insurance Policies
7) Traffic Signal Management
8) Card Games
Sample Spaces :
Tossing of a coin
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| 1 Rupee Coin - Tail & Head |
H - Head
T - Tail
✅When 1 coin is tossed.
Then we have two possible outcomes
{H,T}
✅When 2 coins are tossed.
Then we have four possible outcomes
{HH, HT, TH, TT}
✅When 3 coins are tossed
The we have eight possible outcomes
{HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}
Rolling of a Die
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|
Rolling of Dice
|
✅When 1 Die is rolled.
Then we have total six possible outcomes.
{ 1,2,3,4,5,6}
✅When 1 Die is rolled.
Then we have total 36 possible outcomes.
{ (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) }
Playing Cards
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| Total Playing Cards in a Deck |
There are total 52 Cards in a deck which are divided into four suits of 13 cards each.
The name of four suits are
1) spades (♠),
2) hearts (♥),
3) diamonds (♦) and
4) clubs (♣)
Clubs and spades are of black colour, while hearts and diamonds are of red colour.
The cards in each suit are ace, king, queen, jack, 10, 9, 8, 7, 6, 5, 4, 3 and 2. Kings, queens and jacks are called face cards.
Maths Class 10 School Activity on Dice Coins & Playing Card | Activity by Chesta
> Introduction
> Define
> Give Examples from day to day life
> Draw or Paste coins
> Sample spaces of
1 Coin
2 Coins
3 Coins
> Die
> Playing Cards
