Use complements and disjoint cases to compare multi-roll targets.
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First lesson in this subject: Count equally likely outcomes
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Game A uses a fair six-sided die with net rewards 0, 0, 0, 0, 0, 12. Game B gives 2 net points every roll. Make 3 independent rolls, using the same game each time.
Both games average 2 per roll. To reach at least 6 in total, B succeeds for certain. A needs at least one 12: of 6³ = 216 equally likely face sequences, 5³ = 125 have none, leaving 91 wins.
You are reading the opening. Members read every lesson and guide in full. A free account reads the first lesson in each subject in full.
You are reading the opening. Your free account reads the first lesson in each subject in full. Members read every lesson and guide in full.
First lesson in this subject: Count equally likely outcomes
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Practice · Try point games and discover when a big prize, a better average and a better chance mean different things.
Book · Count outcomes, update chances with new information, and compare decisions through worked examples.
Previous lesson · Subtract the cost and weight every net outcome by its probability.
Next lesson · Use the chance of no match to understand why shared birthdays arrive surprisingly soon.
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