Coding Grandmaster · project 19 of 46 · premium, free for now

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.

Learn

Probability is favourable outcomes divided by all equally likely outcomes. With two dice there are 6 × 6 = 36 equally likely pairs, so a program can list them all with two loops and count the ones you want. Always simplify the fraction: 6/36 is the same as 1/6, and math.gcd finds the shared factor.

Your task

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.

Stretch challenge

Which total is the most likely? Draw the counts as a bar chart.

← Permission flags The OR rule →

Python

Press Run to see what your program prints.

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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.

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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.

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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.

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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).

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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 Monty Hall Lab

Pick a door, then stay or switch. Play ten games, then run a thousand to see the surprising answer.

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FAQ

Counting outcomes: common questions

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