From Discrete to Continuous

Probability · Axiom Academy

INTRO From Discrete to Continuous Exploring the world of infinitely many possibilities. Let's start with something familiar. Roll a standard die and observe the outcome. Click the button to roll multiple times. Now imagine measuring a person's height in centimeters. Move the slider to see different possible heights. Step 3: The Probability Paradox Let's think about probability. What's the probability of measuring exactly 170.00000... cm? Instead of asking about exact values, we ask about ranges . Adjust the interval to see probabilities. Countable outcomes (dice, coin flips, number of customers). Each outcome has positive probability. We sum probabilities over all possible values. Uncountable outcomes (height, time, temperature). Individual points have zero probability. We measure probability over intervals using areas under curves. Moving from discrete to continuous means shifting from counting to measuring , from sums to integrals , and from points to intervals .

This is the written version of the interactive lesson above. See the full Probability course.