PROBABILITY
INTRODUCTION
— Many
events can't be predicted with total certainty. The best we can say is
how likely they are to happen, using the idea of probability.
— Probably
Kuzhalisai will stand first in the forth coming annual examination. ™
— Possibly
Thamizhisai will catch the train today. ™
— The
prices of essential commodities are likely to be stable. ™
— There is a chance that Leela
will win today’s Tennis match.
— The
words “Probably”, “Possibly” , “Likely”, “Chance” , etc., will
mean “the lack of certainty OR uncertainty”
EXAMPLES
— “Should
I carry an umbrella to work today?”, “Will my cellphone battery last until
tonight?”, and “Should I buy a new brand of laptop?”. Probability provides a
way to make decisions when the person is uncertain about the things, quantities
or actions involved in the decision.
DEFINITION
— Probability
is the chance that something will happen - how likely it is that some event
will happen.
— Sometimes
you can measure a probability with a number like "10% chance of
rain", or you can use words such as impossible, unlikely, possible, even
chance, likely and certain.
FORMULA:
FORMULA:
— Probability
of an event happening = Number of ways it can happen / Total
number of outcomes
EXAMPLES
Throwing Dice :
• When
a single die is
thrown, there are six possible outcomes: 1, 2, 3, 4, 5, 6.
• The
probability of any one of them is 1/6.
• BASIC
CONCEPTS:
• Experiment
• Trial
• Sample
space
• Sample
point
• Events
EXPERIMENT:
v An
experiment is defined as a process whose result is
well defined.
v There
are two types of experiment.
- Deterministic Experiment : It is an experiment whose outcomes can be predicted with certainty, under identical conditions.
- Random Experiment : It is an experiment whose all possible outcomes are known, but it is not possible to predict the exact outcome in advance.
Trial
A Trial is an action which results in one or several outcomes.
EXAMPLES:
“ Flipping” a coin and “Rolling”
a die are trials
SAMPLE SPACE:
A sample space S is the set of all possible outcomes of a
random experiment.
EXAMPLE:
• While
rolling a die, sample space
• S = { 1, 2,3,4, 5, 6}
SAMPLE POINT:
Each outcome of an experiment is called a sample point.
EXAMPLE:
While rolling a die each outcome,
{1} {2} {3} {4} {5}
and {6}
are are corresponding
sample points .
EVENTS:
— Any
subset of a sample space is called an event.
— EXAMPLE:
— When
a die is rolled some of the possible events are {1, 2, 3}, {1, 3}, {2, 3, 5, 6}
APPLICATION:
many ways probability used in our life.
Examples:
- every day you use probability to plan around the weather. Meteorologists can't predict exactly what the weather will be, so they use tools and instruments to determine the likelihood that it will rain, snow or hail. For example, if there's a 60-percent chance of rain, then the weather conditions are such that 60 out of 100 days with similar conditions, it has rained. You may decide to wear closed-toed shoes rather than sandals or take an umbrella to work. Meteorologists also examine historical data bases to guesstimate high and low temperatures and probable weather patterns for that day or week.
- I’ve Got Your Number:
- Produced in collaboration with Wales Institute of Mathematical and Computational Sciences, I’ve got your Number is a quiz show with a difference. Thank you.
