Applicaon of probability in day to day life

application of probability in our daily life

1. Name = D ipanshu Chaurasiya class/sec = 9/d Topic = Application of probability in day to day life

2. History of probability 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 Pierre de Fermat, this becoming the first evidence of probability

3. Probability originated from the study of games of chance. Tossing a dice or spinning a roulette wheel are examples of deliberate randomization that are similar to random sampling. Games of chance were not studied by mathematicians until the sixteenth and seventeenth centuries. Probability theory as a branch of mathematics arose in the seventeenth century when French gamblers asked Blaise Pascal and Pierre de Fermat (both well known pioneers in mathematics) for help in their gambling. In the eighteenth and nineteenth centuries, careful measurements in astronomy and surveying led to further advances in probability .

4. Emergence of probability All the things that happened in the middle of the 17 th 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.

5. MODERN USE OF PROBABILITY In the twentieth century probability is used to control the flow of traffic through a highway system, a telephone interchange, or a computer processor; find the genetic makeup of individuals or populations; figure out the energy states of subatomic particles; Estimate the spread of rumours; and predict the rate of return in risky investments.

6. Predictable and unpredictable occrrence Predictable Occurrences: The time an object takes to hit the ground from a certain height can easily be predicted using simple physics. The position of asteroids in three years from now can also be predicted using advanced technology. Unpredictable Occurrences: Not everything in life, however, can be predicted using science and technology. For example, a toss of a coin may result in either a head or a tail . In these cases, the individual outcomes are uncertain. With experience and enough repetition, however, a regular pattern of outcomes can be seen (by which certain predictions can be made).

7. What is probability Probability is a measure of how likely it is for an event to happen . We name a probability with a number from 0 to 1 . If an event is certain to happen, then the probability of the event is 1. If an event is certain not to happen, then the probability of the event is 0. We can even express probability in percentage.

8. chance Chance is how likely it is that something will happen. To state a chance, we use a percent. Certain not to happen ---------------------------0 %. Equally likely to happen or not to happen ----- 50 %. Certain to happen ----------------------------------- 100 %.

9. Example of chance When a meteorologist states that the chance of rain is 50%, the meteorologist is saying that it is equally likely to rain or not to rain. If the chance of rain rises to 80%, it is more likely to rain. If the chance drops to 20%, then it may rain, but it probably will not rain . Donald is rolling a number cube labelled 1 to 6. Which of the following is LEAST LIKELY? an even number an odd number a number greater than 5

10. Possible outcomes. 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.

11. event 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.

12. favourable event The no. of outcome which result in the happening of a desired event are called favourable cases of the event. Example:- In a single throw of a dice ,the no. of favourable cases of getting an odd no. are three.

13. Relative Frequency Relative 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.

14. Conditional probability 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.

15. RANDOM PHENOMENON An event or phenomenon is called random if individual outcomes are uncertain but there is, however, a regular distribution of relative frequencies in a large number of repetitions. For example, after tossing a coin a significant number of times, it can be seen that about half the time, the coin lands on the head side and about half the time it lands on the tail side. Note of interest: At around 1900, an English statistician named Karl Pearson literally tossed a coin 24,000 times resulting in 12,012 heads thus having a relative frequency of 0.5005 (His results were only 12 tosses off from being perfect!).

16. Example of probability When a meteorologist states that the chance of rain is 50%, the meteorologist is saying that it is equally likely to rain or not to rain. If the chance of rain rises to 80%, it is more likely to rain. If the chance drops to 20%, then it may rain, but it probably will not rain. Donald is rolling a number cube labelled 1 to 6. Which of the following is LEAST LIKELY? an even number an odd number a number greater than 5

17. Formulae Of Probability • A dice is thrown 1000 times with frequencies for the outcomes 1,2,3,4,5 and 6 :- Ans. Let Eid denote the event of getting outcome i where i=1,2,3,4,5,6:- Then; Probability of outcome 1= Frequency of 1 Total no. of outcomes = 179 1000 = 0.179 Therefore, the sum of all the probabilities , i.e., E1 + E2 + E3+ E4+ E5 + E6 is equal to 1……….

18. T H A N K Y O U A L L F O R W A T C H I N G