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When we come across these types of statements, we enter into the world of probability that has been studied by mathematicians for hundreds of years.

A lot of our decisions involve probabilistic considerations and most of the time, we are not even aware that we are taking them into account. This is well

reflected in our language, with phrases like, ‘I have a good feeling about this’, ‘I might get lucky today’, ‘this sounds good’, ‘this might be our day’, etc. So we

can say that “probability” or “chance” is very commonly used term and prevalent in our daily life conversations.

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Cyclone More ‘Likely’ To Cause Heavy Rain In Northeast, Odisha

Why It Is The Best ‘Chance’ For England To Win The World Cup?

Vladimir Putin ‘Probably Approved’ Killing of Former Russian Spy : British judge

The “chance” plays a dominant role in many aspects of daily life, whetherbuying insurance policies, playing games, investing in stock markets orchoosing a seat on your next flight. We sometimes choose between options"at random“.

Many outcome can't be predicted with absolute sureness. The best we can say ishow likely they are to happen, using the idea of probability. A basicunderstanding of probability help us to understand everything from battingaverages to the weather report or your chances of being struck by lightning!Probability is an important topic in mathematics because the probability ofcertain events happening - or not happening - can be important to us in the realworld.

PREDICTING THE WEATHERWhile predicting the weather we think about the ‘chances’ that it will rain today, we examine whether there are dark clouds in the sky, by

observing wind, air or humidity etc. However, the beliefs that we form are based on these factors may vary from person to person - different

people may make different estimates of the probability that it will rain.

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Line of Probability

Example

Probability can range in between

0 to 1, where 0

probability means the

eventto be an

impossible and

probability 1 indicates the certain

event.

Have you ever went for camping in the rain? If not, Imagine it!

You are sitting in a tent, rain pouring down heavily. You havenothing to do - the weather report was wrong and you wishthat you had visited another weekend for this experience. Aswe all know, predicting weather is not an exact science. Theweather is an example of a random phenomena.Random phenomena are occurrence that vary from day-to-dayand case-to-case. Besides weather, rolling dice in games,drilling for oil and driving your car are all examples of randomphenomenon.

Probability is the measure of the likelihood of an event to occur. Many events cannot be predicted

with total certainty. We can predict only the chance of event to occur, how likely they are to

happen, using probability.

Although we never know exactly how a random phenomenon will turn outbut we can calculate it in a certain way using probability

Source:

https://byjus.com/maths/probability/

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ODDS OF PROBABILITY

What are the odds against surviving an

Airplane Crash?

The Odds against surviving an Airplane CrashThe safest place to be seated in the event of an airplanecrash is in an aisle seat above the wings. In this case, theprobability of surviving the crash is 56%. What are theodds against you surviving?

The odds against you surviving are the probability of younot surviving versus the probability of you surviving.

Thus ,the odds against you surviving are 11 to 14

Reference: “Mathematics all around” ch : 13

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The law of large numbers If we perform the same experiment a large number of times, average ofthe results obtained becomes close to the expected value.=> The more we roll the die, the closer we will get to the outcome weexpect to come. We call it the Law of Large Numbers.

ACTIVITY TRY YOURSELF

Flip a coin 10 times and record how many times it lands on heads and how many times it lands on tails.

Heads: ____________ Tails: ____________ Now flip it 100 times and record your results.

Heads: ____________ Tails: ____________

Did you get closer to a ½ ratio the second time? That’s the Law of Large Numbers at work. Remember, the Law of Large Numbers tells us that the

more times you repeat an experiment, the closer the relative frequency will come to the probability.

Relative Frequency

Relative frequency means how often something happens divided by all outcomes.

Example: If your team has won 9 games from a total of 12 games played;

• the Frequency of winning is 9• the Relative Frequency of winning is 9/12 = 75%

Reference: https://www.mathsisfun.com/definitions/relative-frequency.html

Definition:An experiment is any observation of a random phenomenon.The different possible results of the experiment are called outcomes.The set of all possible outcomes for an experiment is called a sample space.

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CONDITIONAL PROBABILITY

Conditional probability takes into account that one event occurring may change theprobability of a second event.Let’s understand how occurrence of one event can affect the probability of anotherevent. Suppose that you and your friend Samir betting over a Mystery novel. Tosettle the matter both of you decided to roll a pair of dice. You will each pick anumber and then roll the dice. The person whose number comes 1st as the total onthe dice will win. As you know that number 7 has highest probability because it hashighest probability of appearing namely 1/6.

To illustrate the idea of conditional probability,let’s change this situation slightly.

Assume that your friend Anil will roll the dice before you and Mahi pick yournumbers. You are not allowed to see the dice, but Anil will tell you something aboutthe dice and then you will choose your number before looking at the dice.Suppose Anil tells you that the total showing is an even number. Would you choose a7? Certainly not! You know the condition that total is even, you will exclude all pairsfrom the sample space such as (1,4), (5,6), and (4,3) that give odd totals.

In a similar way, suppose that you draw a card from a standard 52-card deck, putthat card in your pocket, and then draw a second card. What is the probability thatthe 2nd card is a King? How you answer this question depends on knowing what cardis in your pocket. If the card in your pocket is king, then there are three kingsremaining in the 51 cards that are left, so the probability is 3/ 51. If the card inyour pocket is not a king, then the probability of the 2nd card being a king is 4/ 51.

Hence, when we compute the probability of event F assuming that the event E hasalready occurred, we call this the conditional probability of F given E,We denote this probability as P(F/E). We read this as “ the probability of F giventhat E has occurred”

Reference: Mathematics all around, chapter : 13

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Probability In Daily Life

Weather forecast

• Nearly every day you use probability toplan around the weather.Meteorologists can't predict exactlywhat the weather will be, so they usetools and instruments to determine thelikelihood that it will rain, snow or hail.For example, if there's a 60-percentchance of rain, then the weatherconditions are such that 60 out of 100days with similar conditions, it hasrained. You may decide to wear closed-toed shoes rather than sandals or takean umbrella to work. Meteorologistsalso examine historical data bases toguesstimate high and low temperaturesand probable weather patterns forthat day or week.

Sports Strategies

• Athletes and coaches use probabilityto determine the best sportsstrategies for games and competitions.If a high-school football kicker makesnine out of 15 field goal attempts fromover 40 yards during the season, hehas a 60 percent chance of scoring onhis next field goal attempt from thatdistance. The equation is: 9 / 15 =0.60 or 60 percent

Referred from https://classroom.synonym.com/real-life-probability-examples-7719506.html

To decide whether it is worth taking some action and what action to take, we relyon a measure of the likelihood of an event on a daily basis. The practicalsituations for most of us relate to games of chance, anything from a game ofLudo to a game of Roulette. On the other hand, businesses such as insurancecompanies need to know about events concerned with car accidents, death, andfootballers having accidents.

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Probability In Daily LifeInsurance Options

Games and Recreational Activities

• We use probability when we plays ludo, cardgames or video games that involve luck orchance. You must weigh the odds of gettingthe cards you need in poker or the secretweapons you need in a video game. Thelikelihood of getting those cards or tokenswill determine how much risk you're willing totake.

Reference: https://classroom.synonym.com/real-life-probability-examples-7719506.html

TRY YOURSELF

Look at probability in the media like popularity ratings

(who is most preferred for Prime Minister), the use of

probability in medicine (35% of people over 60 will die of

cancer), and other applications of probability.

Probability plays an important role inanalyzing insurance policies to determinewhich plans are best for you or your familyand what deductible amounts you need.For example:-(1) When choosing a car insurance policy, youuse probability to determine how likely it isthat you'll need to file a claim.(2) If 12 out of every 100 drivers or 12percent of drivers in your community havehit a deer over the past year, you'll likelywant to consider comprehensive insurance onyour car. You might also consider a lowerdeductible if average car repairs after adeer-related incident run Rs. 2,800 and youdon't have out-of-pocket funds to coverthose expenses.

Air pollution is triggering diabetes in 3.2 million people each year

Fine particulate matter, belched out by carsand factories and generated throughchemical reactions in the atmosphere, hangaround as haze and make air hard tobreathe. The new estimate, reported inJuly in The Lancet Planetary Health, holdsair pollution responsible for about 14percent of new cases of diabetesworldwide. Factors such as genetics,weight, activity level and diet also influencethe risk of the disease, which is on the riseglobally. (The World Health Organizationestimates that 422 million people now livewith type 2 diabetes — up from 108 millionin 1980.)For more details visit-https://www.sciencenews.org/article/air-pollution-triggering-diabetes-in-millions-each-year Image Source: NASA

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ADDING TO YOUR KNOWLEDGE

SATYENDRA NATH

BOSE

Indian physicist Satyendra Nath Bose

is known for working with Albert Einstein on the

Bose-Einstein Condensate

Satyendra Nath Bose was born on January 1, 1894 in Kolkata, India. A

renowned Indian physicist, he specialised in theoretical physics. He is best known

for his work on quantum mechanics in the early 1920s, providing the foundation for Bose-Einstein statistics and the theory

of the Bose-Einstein condensate.He was awarded India's second highest civilian award, the Padma Vibhushan in 1954 by the Government of India. The

class of particles that obey Bose-Einstein statistics, bosons, was named

after Bose.

RESPONSE SHEET

1) Why calculating probability of events is important in our daily life?

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2) Give an example from your daily life where you have used probability unknowingly?

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3) Assume that you roll two dice and the total showing is greater than nine. What is theprobability that the total is odd?

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RESEARCH WORK

Explore on the topic “Probability and Genetics” and explain in your own language.

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YOUR FEEDBACK

My Name: _______________________________________________

I am in class: __________________

From School: ______________________________________________

Topics well explained in this issue:

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Topics need more explanation in this issue:

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Suggest next Theme:

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Any other:

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PROJECT TEAM

Dr. Jyoti Sharma , Prof. Pankaj Tyagi , Prof. Shobha Bagai , Prof. Bibhu Biswal

Email id: giftededucationcic@gmail.com

RESEARCH TEAM

Shilpi Bariar, Sreelatha S. Narayanan, Anurag Saini, Davinder Kaur, Shantanu Joshi, Uzma Masood

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