Calculating Probabilities using Python 20 out of 20

[x5960114061]

https://www.codecademy.com/paths/data-science/tracks/dsf-statistics-fundamentals-for-data-science/modules/dsf-probability-for-data-science/lessons/introduction-to-probability-distributions/exercises/calculating-probabilities-using-python

So in this exercise I was just playing around with the code to see the different answers I would get. When I picked x = 20 and n = 20 I got 9.5367431640625e-07 shouldn’t it be closer to 0.0 I mean the chance of getting 20 heads in 20 trials has to be pretty rare to the point of it never happening so why this 9.536 number?

I also noticed that when I did x = 1 and n = 5000 I get 0.0 which to me makes more sense. The chance of getting 1 head in 5000 flips would never happen.

Here is the code.

x = 20
n = 20

prob_2 = stats.binom.pmf(x, n, 0.5)
print(prob_2)

[janbazant1107978602]

The e-07 at the end means 10^-7 (scientific notation)
so 9.5e-07 is the same as 0.00000095 (notice the 6 zeros after the decimal point)
which is very close to 0

Summary

9.5e-07 = 9.5 × 10^-7 = 0.000 000 95