Probability as Frequency

Part of the Statistics for ML section of Coddy's Machine Learning journey. Lesson 13 of 64.

A spam filter says "90% spam"; a seed packet says "80% sprout". A probability is a long-run share, from 0 (never) to 1 (always). Here are 50 seeds:

50 seeds as a grid of cells: 41 dark cells sprouted and 9 pale cells marked x did not, a share of 0.82 for a chance of 0.8

rng.random(n) draws decimals from 0 to 1, and 80% of them land below 0.8. So one comparison plants 1000 seeds:

rng = np.random.default_rng(3)
sprouted = rng.random(1000) < 0.8
print(sprouted.sum())
print(sprouted.mean())

This prints:

814
0.814

The mean of booleans is the share of True: 0.814, near 0.8. By this chapter's end, that trick prices a whole dice stall.

Challenge

Medium

A striker scores a penalty with some chance. The program reads the chance (0 to 1), then the number of kicks; the starter makes rng.

Simulate the kicks: a goal wherever a rng.random draw is below the chance.
Print the goals and the estimated chance, rounded to 3 decimals.

For 0.5 and 10 kicks, a short run that wobbles far from 0.5:

Goals: 3 of 10
Estimated chance: 0.3

Try it yourself

import numpy as np

chance = float(input())
kicks = int(input())

# Don't change the line below
rng = np.random.default_rng(21)

# Write your code below

Test yourself

This lesson includes a short quiz. Start the lesson to answer it and track your progress.

All lessons in Statistics for ML

3Probability by Simulation

Probability as FrequencyThe Law of Large Numbers Sums of Dice Expected Value Conditional Probability Recap: Dice Stall Odds

6Relationships

Reading Scatter Plots Correlation Correlation Matrix Correlation Heatmaps Correlation Is Not Cause Recap: Ice Cream and Sun

9Feature Scaling

Why Scale Features Min-Max Scaling Standardization StandardScaler Recap: Climbing Partners

12Final Challenges

Train Delays Air Quality Wine Chemistry Clinic Survey

Practice on your own: Online Python compiler