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Introduction to Computational Thinking and Data Science
Optimization
01Optimization Models and the Knapsack Problem02Brute-Force Knapsack and the Exponential Power Set03Greedy Algorithms: One Function, Any Definition of Best04Lambda Keys and Why Greedy Can Miss the OptimumProblem setMIT problem set
01The Knapsack Search Tree: Every Combination, 2ⁿ Nodes02Recursive maxVal: An Exhaustive Search That Beats Greedy03Memoization: Turning Slow Fibonacci into fastFib04Overlapping Subproblems and the Memoized KnapsackProblem setMIT problem set
Graph Models
01Graphs as Models: Nodes, Edges and Euler's Seven Bridges02Coding a Graph in Python: Node, Edge, Digraph and Graph03Depth-First Search for the Shortest Path in a Graph04Breadth-First Search: A Queue of Paths, Fewest Hops FirstProblem setMIT problem set
Stochastic Thinking
01Predictive Nondeterminism and the Stochastic Die Roll02Probability as Counting, and When Multiplying Fails03Simulating Rare Events: Random Seeds and Many Trials04The Birthday Problem: Formula Versus SimulationProblem setMIT problem set

Probability as Counting, and When Multiplying Fails

Why is 11111 exactly as likely as any other five rolls, and when does multiplying probabilities give a bogus answer?


Finger exercises

Short drills on what this video just taught. Write the code, run the checks, and reveal the answer only if you are stuck.

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Exercise 1 of 5

How likely is 11111

Count the possible outcomes of five rolls of a six-sided die, then divide to get the probability that the five rolls come out exactly 11111. Assign the count to outcomes and the probability to p.

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rolls = 5
faces = 6
outcomes = ...  # your code here
p = ...

Python runs in your browser
⌘/Ctrl + Enter runs
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outcomes is an int
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counts every outcome of five rolls
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p is one outcome out of all of them
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