- Education and Science
Probability of Life
Probability is the study and calculation of how often and why certain man-made and natural events occur. Those events that are once deemed to be random and unpredictable are now turned out to be just the opposite. Everything in Nature operates in accordance to a set of rules. Human beings are the only things in Nature who have unveiled, comprehended, and utilized these rules to better their chance of survival. From Newton’s Classical Mechanics that enables humans to understand motions and forces on Earth, to Einstein’s General Theory that helps humans to explore the universe, and to Quantum Mechanics that uncovers the world of the subatomic, they are some of the examples of Nature’s rules that have helped to advance human’s civilization to the next level.
We all know that a coin has two sides each having a different pattern. One side is called Head (H) and the other is called Tail (T). When the coin is flipped and landed on a flat surface, the chance of H showing face-up is 50% and the same is true for T. Since there are 2 choices (H, T) in the flipping-coin event, the Probability (P) of 1 of the choice to occur is equal to 1 over 2 or P = ½ = 0. Let us consider the following cases:
1) If the coin is flipped twice, what is the Probability that H will occur at least once?
P = ½ + ½ = 1.
2) If the coin is flipped twice, what is the Probability that H (H_H) will occur 2 times?
P = ½ x ½ = ¼ .
The same result applies for the occurrence of H_T, T_H, and T_T.
3) If the coin is flipped N times, what is the Probability that H will occur N times?
P = ½ x - - - x ½ = 1/2N ≈ 0, as N becomes bigger and bigger.
4) When 4 people are flipping a coin 2 times simultaneously, the Probability that H_H can be found in one of the 4 people is calculated as
P = ¼ + ¼ + ¼ + ¼ = 1.
The Poker card game is played with the standard poker cards. Even though there are many different ways to play Poker, the winning hand is basically determined by the ranking of the 5 card combination as followed:
a) ROYAL-FLUSH (RF) – Ace, King, Queen, Jack and 10 in ranking sequence of the same suit;
b) STRAIGHT-FLUSH (SF) - five cards in ranking sequence of the same suit with no Ace;
c) FOUR-OF-A-KIND (4OK) – four cards of the same rank with one card of anything;
d) FULL-HOUSE (FH) – three cards of the same rank and two cards of the same rank;
e) FLUSH (FL) - five cards of the same suit of random ranking sequence;
f) STRAIGHT (ST) - five cards in ranking sequence of different suits;
h) THREE-OF-A-KIND (3OK) - three cards of the same rank with two cards of anything;
i) TWO PAIRS (2P) – two pair of two cards of the same rank with one card of anything;
j) ONE PAIR (1P) - two cards of the same rank with three cards of anything.
k) NOTHING (NOT) - five cards of anything.
The reason that RF has the highest ranking is because the Probability of its occurrence is the lowest comparing to the other 5 card combinations. Its Probability is calculated as followed:
1) Since there are 52 cards in Poker, the Probability of A’s choice to occur is 4 over 52; namely, A of Spade (S), A of Heart (H), A of Diamond (D), A of Club (C).
2) The 1st card can be either A’s, K’s, Q’s, J’s, or 10’s, so, PRF1 = (5X4)/52 = 20/52.
3) The 2nd card can only be 4 of the 5 with 51 cards left, so, PRF2 = 4/51.
4) By the same token, PRF3 = 3/50, PRF4 = 2/49, PRF5 = 1/48.
5) Finally, PRF = PRF1 x PRF2 x PRF3 x PRF4 x PRF5
= 20/52 x 4/51 x 3/50 x 2/49 x 1/48 .
The Probability for SF is calculated as followed:
1) The 1st card can be anything but A’s, so, PSF1 = (52-4)/52 = 48/52.
2) The 2nd card can only be 4 of the 5 with 51 cards left, so, PSF2 = 4/51.
3) By the same token, PSF3 = 3/50, PSF4 = 2/49, PSF5 = 1/48.
4) Finally, PSF = PSF1 x PSF2 x PSF3 x PSF4 x PSF5
= 48/52 x 4/51 x 3/50 x 2/49 x 1/48 .
The Probability for 4OK is calculated as followed:
1) The 1st card can be anything, so, P4OK1 = 52/52 = 1.
2) The 2nd card can also be anything, so, P4OK2 = 51/51 = 1.
3) The 3rd card can only be the same ranking as the first 2 cards, so, P4OK3 = (2x3)/50 = 6/50.
4) The 4th card can only be the 2 remaining quad, so, PSF4 = 2/49.
5) By the same token, P4OK5 = 1/48.
6) Finally, P4OK = P4OK1 x P4OK2 x P4OK3 x P4OK4 x P4OK5
= 1 x 1 x 6/50 x 2/49 x 1/48 .
So, the conclusion is that PRF < PSF < P4OK - - - - < P1P < PNOT .
If a special typewriter can be built to randomly and automatically type one of the 26 alphabets or a space then advance to the next position to repeat the operation. At the end of the 11th character, it skips to the next line and repeats typing the 11 characters randomly and automatically. If the typewriter can execute the above operations for a long time, what is the chance of seeing the phrase, HOW ARE YOU, appears in one of the lines? The answer lies in the Probability.
Since there are 26+1 choices, PPHRASE = 1/27 x 1/27 x - - - - x 1/27 = 1/2711. So, the Probability states that it will take this typewriter to type no more than 2711 times to see the phrase, HOW ARE YOU, for certainty. Assuming that it takes 1 second for this typewriter to type 1 character, the occurrence is translated to 2711 seconds, or ≈ 176 million years. But, if we can build 2711 such typewriters and have them all start typing at the same time, we will be able to see the phrase, HOW ARE YOU, appearing on one of the 2711 typewriters in 11 second! (It is just like winning the Lotto. If you buy one ticket, the chance of hitting the jackpot is around 1 in 100 millions. But, when there are around 100 million people each buying one ticket, the chance that someone will hit the jackpot is close to 100 %. )
Following the same logics, more complex phrases, sentences, or even books can be produced in this fashion in a reasonable time by employing faster and more typewriters.
Every living thing on Earth has a unique set of DNA that is responsible for its makeup. DNA is made of two long chains of nucleotides joining together by A, C, T, G base pairs in specific orders. It is now known that all land animals including human beings were evolved from the fish. The DNA composition between the fish and human being is more or less the same. The differences lie in the arrangement of the base pairs A, C, T, and G in specific regions of the DNA. Nature introduced these changes in small and incremental steps through a random process called mutation during reproduction. This random process had taken over 4 billion years with abundance of working samples. It can be explained in principle by the aforementioned Probability of the Coin, Poker, and Typewriter, as it takes longer time to come up with the equivalent of the Royal Flush like in the Poker case or a Shakespeare's play like in the Typewriter example.
Probability can be used to explain the underlying mechanism of the diversity of life found on Earth. But, it is more than a chance happening. The process is also guided by a set of Nature’s rules and conditions. They all have to work seamlessly together for life to flourish, multiply, and evolve. The crowning achievement after 4 billion years of mixing and meshing is the emergence of an intelligent life form called human being. Humans are not only able to understand the whole evolution process and its rules but also to ponder the logic that if the design has intelligence then there must also be intelligence behind the design . This intelligence may well be higher than their own and may even be incomprehensible and unimaginable. In the meantime, human race, collectively, has transformed Nature’s landscape and uncovered its rules one by one thinking that its destiny is in its own hand and life can be more than just survival of the fittest.