Coding Grandmaster · project 20 of 46 · premium, free for now

The OR rule

Build the 52-card deck as (rank, suit) pairs, then count the cards that are the chosen suit, the chosen rank, both, and either. Print the four counts and the chance of either as a fraction in lowest terms.

Learn

P(A or B) = P(A) + P(B) − P(A and B). You subtract the overlap because outcomes that are in both groups get counted twice when you add. A deck of cards shows it clearly: hearts and kings overlap in exactly one card, the king of hearts.

Your task

Stretch challenge

Prove with code that either == suit_count + rank_count - both for every suit and rank.

← Counting outcomes Given that… →

Python

Press Run to see what your program prints.

Keep going in Coding Grandmaster

Counting outcomes

Write ways(target), the number of dice pairs that add up to target, and as_fraction(top, bottom) that returns text like 1/6 in lowest terms. Print the chance of a total of 7.

Start →21

Given that…

For the chosen club print how many students are in it, how many passed, and P(passed | club) as a percentage with one decimal place. Then print P(passed) for all students.

Start →22

Bayes and the medical test

Write posterior(prior, sensitivity, specificity) returning P(sick | positive) rounded to 4 decimal places. Print it for prior 0.01, sensitivity 0.9, specificity 0.9.

Start →23

The binomial distribution

Write binomial(n, k, p) and use it to print the chance of exactly 3 heads in 5 fair flips, the chance of at least 4 heads, and the total of all the chances (rounded to 6 places).

Start →24

How computers fake randomness

Write next_value(seed) with that formula, and roll(seed) = 1 + seed % 6. Starting from the given seed, roll 600 times (feeding each result back in) and print how many times each face 1 to 6 came up.

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Practise the idea

🃏 Play Maths Memory Match

Flip cards to match each sum with its answer. Times tables, addition, fractions and percentages.

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FAQ

The OR rule: common questions

I am stuck. What can I do?

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