Holidays’ Homework Project

Made By:- JAYANT NAMRANI IX – A

Rainbow English School C-3, Janak Puri, New Delhi-110058

Example of any Real Life Situation to connect it with any topic of Mathematics.

PROBABILITY

Probability is an area of mathematics which we use all the time in daily life – and usually without thinking about it. While many aspects are very intuitive, probability becomes much more difficult when thinking about it in a precise, mathematical way. The easiest definition is that probabilities are numbers between 0 and 1 which specify the chance that something happens. A probability of 0 means that something is impossible; a probability of 1 means that something is certain.

It is certain that the Earth will still exist tomorrow and impossible that you will meet a basilisk. A coin landing heads or a die rolling 6 have probabilities in between 0 and 1. However, when tossing a coin, it will either land heads or it will land tails. So why isn’t the probability either 1 or 0 – rather than a number in-between? Or suppose we toss a coin but don’t look at it. For us, the probability of landing heads is still 0.5, even though it has already happened!

These questions can be answered by thinking about the various different ways in which we can interpret probabilities.

Tossing Coins and Rolling Dice

Even if we ignore quantum mechanics, coins never have exactly the probability 0.5 of landing heads. Maybe it is 0.4856, maybe it is 0.500012, depending on their physical properties.

In mathematics we don’t have to worry about the underlying physics or tiny inaccuracies. We simplify the real world and build a mathematical model: an imaginary “mathematical coin”, for example, has exactly the probability 0.5 of landing heads and is truly random. This allows us to answer much more interesting questions – such as the probability of three coins landing the same way up.

EXAMPLE

• There are 5 marbles in a bag: 4 are blue, and 1 is red.

What is the probability that a blue marble will be picked?

Solution:-Number of ways it can happen: 4 (there are 4 blues)Total number of OUTCOMES: 5 (there are 5 marbles in the bag)So, the Probability = 4/5 = 0.8

Probability always exists between 0 And 1.

PROBABILITY LINE

Let’s Take Another ExampleQ. Toss a coin 100 times, how many Heads will come up?

Sol.Probability says that heads have

a ½ chance, so we would expect 50 Heads.

But when you actually try it out you might get 48 heads, or 55 heads ... or anything really, but in most cases it will be a number near 50.

Thank You !

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