I built a short presentation demonstrating the use of CodeSkulptor3 (Python 3).
Feel free to follow the links and to offer a critique.
CodeSkulptor3 is a free Python language 'sandbox' for messing around with simple programs
Probability of finding exactly one digit “7” in the range of numbers from 0 to 10^x exclusive
Example 1:
probability in the range of numbers from 0 to 9 (all one-digit numbers)= 0.10
[7]
Example 2:
probability in the range of numbers from 0 to 99 (all two-digit numbers)= 0.18
[7, 17, 27, 37, 47, 57, 67, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 87, 97]
Link to my coding screenshot
Link to my chart screenshot
Code Text
# digit we are trying to match
match = '7'
# my_maxes will be a list from 10 to 10^30
# my_maxes = [10, 100, 1000 ... ]
my_exponents = range(31)
my_maxes = [10**k for k in my_exponents]
# verify
print(my_exponents)
print(my_maxes)
xs = [e for e in my_exponents]
ys = []
for exponent in my_exponents:
ans = (exponent)*9**(exponent-1)
possible = 10**exponent
ratio = exponent/10*0.9**(exponent-1)
#print(possible, ans, ans/possible)
ys.append(ratio)
print(exponent, possible, ans, ratio)
print("\n---")
import simpleplot
# verify
print(xs)
print(ys)
dataset = list(zip(xs,ys))
# verify
print(dataset)
# pops up a line plot
simpleplot.plot_lines('My Answer', 400, 300, 'exponent of 10', 'probability', [dataset], True)