Download Probabilities ...and Proteins

The Smallest and The Largest
•
•
•
•
•
•
•
Mass of an electron
Diameter of living cell
Mass of water
Distance to the sun
Speed of light
National debt
Evolutionary time
(30 billion years)
• Number of atoms in a mole
• Number of electrons in the
conceived universe
9.11
2
.0
9.3
3.0
6
1
x 10-31
x 10 - 8
x 10 0
x 10 7
x 10 8
x 10 12
x 10 18
6.02 x 10 23
1 x 10 80
kilograms
inches
grams/cc
miles
meters/sec
dollars
seconds
Powers of Ten
10 -18
10 -15
10 -12
10 -9
10 -6
10 -3
10 -1
Name
atto ….
femo….
pico….
nano….
micro….
milli….
tenth….
10 18
10 15
10 12
10 9
10 6
10 3
10 1
Name
quintillion
quadrillion
trillion
billion
million
thousand
ten
The Evolutionary Premise (I)

“…However improbable we regard (an)
event …given enough time it will
almost certainly happen at least once ...
Time is in fact the hero of the
plot…given so much time, the
impossible becomes possible, the
possible probable, ad the probable
virtually certain. One has only to wait:
time itself performs miracles.”
Dr. George Wald
Evolutionary Premise (II)

“That which has a probability of one
percent in a year, such as a 100 year
flood, has a 66 percent chance of
occurring in 100 years and a 99 percent
chance of occurring in 1000 years”
Dr. K. E. Boulding
Statistical Evaluation (I)
For independent, repeated trials of an
experiment with two outcomes, success (p)
or failure (q), the probability of a number of
successes, k, from a number of trials, n, with
a probability, p, for each trial is
b = ( n, k ) p k q n - k
Statistical Evaluation (II)
The probability of no successes, k=0, is
b=qn
Therefore the probability of at least one
success is
b=1-qn
For large probabilities, such as Boulding uses,
calculations follow his premise, but for small
probabilities, “virtually certain” success is an
illusion.
For p = 0.01 and n =100 & 1000
1 - q n = 1 - (.99) 100 = 1 - .36603 = 0.634 = 64.3%
1 - q n = 1 - (.99) 1000 = 1 - .00004 = 0.99996 = 99.9%
For p = 0.001 and n = 100 & 1000
1 - q n = 1 - (.999) 100 = 1 - 0.9048 = 0.0952 = 9.52%
1 - q n = 1 - (.999) 1000 = 1 - 0.3677 = 0.6323 = 63.23%
Protein Translation
A Small Protein
Assume a protein of only 100 amino acids (a
very small protein). With 20 amino acids the
number of possible arrangements of these
would be 20100.
20100 = 100130 (approx)
For a specific protein, only ONE of these
100130 possibilities is possible.
So, the probability of getting a particular
protein by random chance is
1
p = ------ = 0.00000.....130 zeros ..1
10 130
= probability of success
q = 1 - p = 0.99999....130 nines
= probability of failure
For repeated random trials, the
probability for at least one
success would be
n
1 - q
n

1

= 1 -  1 - ------- 

10 130 
To offset this improbability, evolutionary theory
demands long time spans. But, even with repetitions
a billion times second for 30 billion years the
probability is still infinitesimally small, as
for n = 10 18 x 10 9 = 10 27
1 - q n = 1 - (0.999.....130 nines..) ^ 10 27
And,
p = 1 - qn

1
 1027
= 1 -  1 - ------- 
= 10 -103

10 130 