ProbabilityProbability

By: Achint BhagatBy: Achint Bhagat

What Is ProbabilityWhat Is Probability?

Probability is a numerical measure of the Probability is a numerical measure of the likelihood that an event will occur, or a way of likelihood that an event will occur, or a way of expressing knowledge or belief. expressing knowledge or belief. For example think about tossing a coin. What For example think about tossing a coin. What are the chances of getting a head and what are are the chances of getting a head and what are the chances of getting a tail?the chances of getting a tail?Since tossing a coin has 2 outcomes, either Since tossing a coin has 2 outcomes, either getting a head or a tail and as both are equally getting a head or a tail and as both are equally likely to occur the probability of getting a head likely to occur the probability of getting a head is ½ and the probability of getting a tail is also is ½ and the probability of getting a tail is also ½. ½.

History History

• The first scientific treatment was given to the The first scientific treatment was given to the subject by Christian Hyugens in 1657.subject by Christian Hyugens in 1657.

• Many mathematician treated the subject as a Many mathematician treated the subject as a branch or a follow up of mathematics. branch or a follow up of mathematics.

• There have been only two ways to formulize There have been only two ways to formulize probability, and they are known as the probability, and they are known as the Kolmogorov formulation and the Cox Kolmogorov formulation and the Cox formulation. formulation.

What Is Probability? (Part 2)What Is Probability? (Part 2)

Probability values are always assigned on a Probability values are always assigned on a scale from 0-1.scale from 0-1.A probability near zero shows an event is unlikely to A probability near zero shows an event is unlikely to

occur. occur.

A probability near one indicates an event is almost certain A probability near one indicates an event is almost certain to occur. to occur.

Other probabilities between zero and one show the degree Other probabilities between zero and one show the degree of likelihood that an event will occur. of likelihood that an event will occur.

Experiments and OutcomesExperiments and OutcomesWhat Is an Experiment?What Is an Experiment?

An experiment is the process by which we generate well defined out An experiment is the process by which we generate well defined out comes or i.e. an experiment leads to results called outcomes.comes or i.e. an experiment leads to results called outcomes.Outcomes are the results of an experiment and an event is one or Outcomes are the results of an experiment and an event is one or more outcomes of an experiment.more outcomes of an experiment.

Example:Example:

ExperimentExperiment OutcomeOutcomeToss a coinToss a coin Head, tailHead, tailRoll a dieRoll a die 1,2,3,4,5,61,2,3,4,5,6Play a football gamePlay a football game Win, lose, Win, lose, tietie

Example: The probability of event A is the number of ways event A can Example: The probability of event A is the number of ways event A can occur divided by the total number of possible outcomes. occur divided by the total number of possible outcomes.

If you consider rolling die:If you consider rolling die:The experiment is rolling the dieThe experiment is rolling the dieThe events are the numbers 1, 2, 3, 4, 5 or 6The events are the numbers 1, 2, 3, 4, 5 or 6and the out come of getting a single number is 1/6 (event/ # is and the out come of getting a single number is 1/6 (event/ # is outcomes)outcomes)

One Very Important Rule

One important rule in doing probabilities is, the sum of the probabilities of all elementary events or outcomes is always one.For example consider the experiment of playing a football game which has 3 possible out comes; winning, losing, or a tie.The probability of winning is 1/3The probability of losing is 1/3And the probability of a tie is also 1/3If we add all these 3 probabilities we are supposed to get one according to the probability ruleTherefore, 1/3+1/3+1/3= 1

Class Activity

• The Red Bulls have won 3/5 matches, what is the probability of them wining their next match, (in a percentage)?

• In a black bag there are 2 white marbles, 2 purple marbles, 3 yellow marbles and 1 brown marble. If you pick up a marble without looking at it 8 times what is the probability that a brown marble will appear?

Bibliography

• http://en.wikipedia.org/wiki/Probability

• http://en.wikipedia.org/wiki/Probability_theory

• http://www.mathgoodies.com/lessons/vol6/intro_probability.html

• http://www.cut-the-knot.org/probability.shtml

• http://mathforum.org/dr.math/faq/faq.prob.intro.html

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