PROBABILITY IN DAILY LIFE

Introduction A branch of mathematics concerned with the study of

randomness and uncertainity.

It is a measure of how often a particular event will happen if something is done repeatedly.

If an event is certain to happen then its probability is 1.

If an event is not certain to happen then its probability is 0.

Probability is always between 0 and 1.

If you draw a card from a standard deck of cards, what is the probability of not drawing a spade?

In a certain population, 10% of the people are rich, 5% arefamous, and 3% are both rich and famous. A person israndomly selected from this population. What is the chancethat the person is› not rich?› rich but not famous?› either rich or famous?

RANDOM EXPERIMENT A random experiment is a process whose outcome is

uncertain.

Examples:-

Tossing a coin once or several times.

Picking a card or cards from a deck.

Sample Space In probability theory,

the sample space of an experiment or random trial is the set of all possible outcomes or results of that experiment.

The result of a random experiment is called outcome.

Example:-Tossing a coin and getting up

head or tail is an outcome.Throwing a dice and getting a

no. between 1 to 6 is also an outcome.

Any possible outcome of a random experiment is called an event.

The probability of an event, denoted P(E), is the likelihood of that event occurring.

Example:- Performing an experiment is

called trial and outcomes are termed as event.

FAVORABLE EVENT The no. of outcome which result in

the happening of a desired event are called favorable cases of the event.

Example:-

In a single throw of a dice ,the no. of favorable cases of getting an odd no. are three.

Relative FrequencyRelative frequency is

another term for proportion; it is the value calculated by dividing the number of times an event occurs by the total number of times an experiment is carried out.

In many situations, once more information becomes available, we are able to revise our estimates for the probability of further outcomes or events happening. For example, suppose you go out for lunch at the same place with probability 0.9. However, given that you notice that the restaurant is exceptionally busy, then probability may reduce to 0.7.

The XVII century records the first use of Probability Theory.

In 1654 Chevalier was trying to establish if such an event has probability greater than 0.5.

Puzzled by this and other similar gambling problems he called the attention of the famous mathematician Blaise Pascal. In turn this led to an exchange of letters between Pascal and another famous French mathematician Pierrede Fermat, this becoming the first evidence of

probability.

Emergence of probability All the things that happened in the

middle of the 17th century, when probability “emerged”: Annuities sold to raise public funds. Statistics of births, deaths, etc.,

attended to. Mathematics of gaming proposed. Models for assessing evidence and

testimony. “Measurements” of the

likelihood/possibility of miracles. “Proofs” of the existence of God.

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