Probability is a numeric representation of how probable / likely an event to occur.
The probability of an event to occur is between 0 and 1, where 0 means “impossible”, “never going to happen”, etc and 1 means that it occurs on each and every try. We can simplify this as, 0<P(an event)<1.
Probability is calculated by dividing the total number of desired outcomes by total possible outcomes.
Let’s take a look at some examples to comprehend further.
Flipping a Coin
We all know that if we flip a coin there is a 50:50 chance that it will be heads or tails. So, the total number of all the possible outcomes is 2, heads or tails. Let’s say our desired outcome is “Heads”, only one out of all outcomes. P(Heads)= ? = 0.5 = 50%. And it is also the same for “Tails”
Rolling a Dice
A dice has 6 faces and each face has a number 1 through 6. So, this time, the total number of all the possible outcomes are 6. Let’s say we would like to know the probability of rolling 5. “5” is the desired outcome out of the total of 6 outcomes. So, P(“5”) = 1/6 = ~0.167
Note that the total of desired outcomes can’t be a negative number and also can’t exceed the total number of all the possible outcomes which means “Numerator” can’t be a bigger number than “Denominator”. Thus, as explained before, the probability of an event occurring is between 0 and 1.
Let’s continue with dice and say we would like to know the probability of rolling a number “Less than 3”. The total number of outcomes is the same as before, 6. But this time, sum of the desired outcomes is 2.
Numbers 1, 2, 3, 4, 5 and 6 are on each face of a dice and the numbers less than 4 are 1 and 2. So, the sum of the desired outcomes is 2(1+1). Note that we are not adding 1 and 2 together and saying “Our numerator is 3”. The number of desired outcomes is 2 because the number of them is 2. There are 2 pieces of desired outcomes.
There could be letters on the faces of dice A, B, C, D, E, F
P(“Less than 3”) = 2/6 = 0.
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This time let’s try to find the probability of getting an even number when rolled a dice. Even numbers on a dice are 2, 4 and 6. There are three desired outcomes so, P(“Even Number”) = 3/6= 0.5
Yet Another Example
The circle above divided evenly into 12 pieces. And we are going to throw a dart on it while it is spinning at a rate that we can’t see the colours so every colour, each and every piece has the same chance of being hit. Each colour has the same probability of being hit, 1/12 (0.08334).
P(“Green Tones”) = 3/12 = 0.25 (As there are 3 green tones on the top right.)
Last One to Correlate with Bitcoin
Let’s completely randomly pick a number between 1 and 10. What is the probability of picking a number less than 3? We have total 10 pieces of numbers and the desires ones are 2 pieces (1 and 2 as they are less than 3)
P(x<3)=2/10 = 0.25 (25%)
Now, let’s randomly pick a number between 1 and 10,000. What is the probability of us picking a number less than 201?
P(x<201) = 200/10000 = 0.02 (2%)
Now, this time let’s use hexadecimal numbers (Base 16).
If you haven’t already, reading about Number systems would be helpful
Yet again let’s pick a random number between 1 and 5F5E100 and calculate the probability of this randomly picked number being less than 10CD23
P(x<10CD23) = ~0.011 (~1.1%)
These simple calculations are essential to the Bitcoin network. With the help of these probability calculations, every Bitcoin block is founded and added to the chain at a roughly 10 minutes interval by adjusting the difficulty.
If you would like to read further:
What is a Hash?
A Simple Expression of the Bitcoin
Thank you for reading. I hope, you enjoyed it and/or it helped you somehow.
Have a nice day :)
