application of probability in our daily life

1. Name =Dipanshu 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 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.

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.

7. 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).

8. 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.

9. 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%.

10. 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

11. 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.

12. 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.

13. 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.

14. 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.

15. 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.

16. 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!).

17. 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

18. 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……….

19. THANK
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