Probability, There are many questions rise about this topic . Why probability is important?, why probability is between 0 and 1?, why probability is hard, how probability is used in real life?,etc.
Probability real life example, If i asks you that you got good marks what will be your parents reaction on this? You will se thay are likely to be happy/proud.
Probability is a concept that helps us understand how likely or unlikely an event is to happen. It's like a way of measuring how often something happens compared to how often it doesn't happens.
So, probability is a very important concept that helps us make predictions and decisions in many different areas of life.
Wait decisions making , How?
In continuation to this example let supposed you were prior told by your parents that if you get good marks you will get that special gift you asked them to give it to you.
So, by getting good marks your parents make decisions yes they will give you that gift.
Now what we will do that we take a coin which have a head on one side and tial on other.
Now just replace good marks to - head
Bad Marks to - Tial
We flip the coin see what we will get?
It is not clear what will be happen? Yes this is all about probability. There is uncertain possibility of event happening.
What we learn till now and what did we know?
1).There are fix possibility of event like coin have only two possibilities 1). Head 2). Tail
2).Any thing can be output of flipping the coin.
So mathematically if you put it in equations
Let say we gave number to it anything head or tail as output is 1.
And max possibility is head + tail = 2.
So, head comes.
P(h) = output/ total output = 1/2.
Now if tial comes
P(t) = output/ total output= 1/2.
Only two possibilities so p(e) = p(h)+ p(t)
P(e) = 1/2 + 1/2 = 1.
Now what is hard in it. As we increase the elements in experiments the complexity may increase in terms of understanding but it is not impossible or really that hard. If you practice few questions you will get the idea of how to look at this topic.
So, that it as introduction to probability. If you want to see video on this you can visit my yt channel -
https://youtube.com/@Fundaofmaths?si=ybiQXbNDdAdrGxJI