Overview Of Probability
Understanding the basics
Dharmanath J. Patil
In this post we will try to understand the basics of probability. We will also see what is sample space? What is a trial/event? What is a experiment? What are the outcomes? and finally what is probability? We will try to understand all these things with a simple example.
Example 1
Let's say we have a fair coin. Fair coin means that there is a equal chance of getting head or tail when you flip a coin. Let's say we want to flip a coin 4 times. So this entire process of flipping a coin 4 times is called experiment and individual flip is called event or trial. In each trial/event there 16 two possibalities. These posibalities are called outcomes. If we want to list all the possible outcomes of this experiment then we wold list them as:
Hence there are 16 possible outcomes. Group of these all possible outcomes is called Sample space.
Let's say if we want to know what is my chance of getting "HHHH" in 4 flips of a fair coin. Then from the above figure
we can say that there is only one chance out of 16. Hence this can be represented as:
P(HHHH) = 1/16
This is called as probability of getting 4 heads in 4 flips of a fair coin.
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Example 2
Let's say we have a fair coin. Fair coin means that there is a equal chance of getting head or tail when you flip a coin. Let's say we want to flip a coin 1 time. So this entire process of flipping a coin 1 time is called experiment and individual flip is called event or trial(Notice: Here experiment consist of one trial unlike example 1). In each trial/event there are two possibalities those are head or tail. These posibalities are called outcomes. If we want to list all the possible outcomes of this experiment then we wold list them as:
Hence there are 2 possible outcomes. Group of these all possible outcomes is called Sample space.
Let's say if we want to know what is my chance of getting "H" in this flip. Then from the above figure
we can say that there is only one chance out of 2. Hence this can be represented as:
P(H) = 1/2
This is called as probability of getting a head in a flip of a fair coin.
. . . .
Example 3
Let's say we have a fair dice. Let's say we want to roll a coin 2 times. So this entire process of rolling a dice 2 times is called experiment and individual roll is called event or trial). In each trial/event there are 36 possibalities. These posibalities are called outcomes. If we want to list all the possible outcomes of this experiment then we wold list them as:
Hence there are 36 possible outcomes. Group of these all possible outcomes is called Sample space.
Let's say if we want to know what is my chance of getting "1,1" in this experiment. Then from the above figure
we can say that there is only one chance out of 36. Hence this can be represented as:
P((1,1)) = 1/36
This is called as probability of getting a (1,1) when we roll a dice twice.
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Observation
From probability we know that there is a 50% chance that you will get a head when you flip a fair coin. But let's say you started flipping a coin and you observer that everytime you flipped a coin it turns out to be tail. So you might feel that probability is not giving you a clear picture. but if you keep flipping a coin probably infinite times, you will definately end up 50% of times head and remaining 50% of times tail.
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Conclusion
Probability can be defined as = Number of possibalities that meet our constraint / total number of possibalities
