Puzzle – Gambler’s Ruin

Which is better - wealth or ability?  Fred Mosteller posed this question in his classic 1965 small compendium Fifty Challenging Problems in Probability, in the context of the Gambler’s Ruin puzzle.  Two players, M and N, engage in a game in which $1 is transferred…

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Pandemic Puzzle – Redux

Late last year, we offered this puzzle, to which no answer was provided at the time: McKinsey recently came out with a study of how a shift to remote learning has affected math test scores of students in elementary school. The impact of school closures…

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PUZZLE OF THE WEEK – School in the Pandemic

This week we offer a puzzle to which I have no answer.  McKinsey recently came out with a study of how a shift to remote learning has affected test scores of students in elementary school. The impact of school closures has been large and negative…

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Puzzle: Surgery or Radiation

Several decades ago, the dominant therapies for lung cancer were radiation, which offered better short-term survival rates, and surgery, which offered better long-term rates. A thought experiment was conducted in which surgeons were randomly assigned to one of two groups and asked whether they would choose surgery. Group 1 was told: The one-month survival rate is 90%. Group 2 was told: There is 10% mortality in the first month. Yes, the two statements say the same thing. What did the two physician groups choose?

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Problem of the Week: Notify or Don’t Notify?

Our problem of the week is an ethical dilemma, posed by the New England Journal of Medicine to its readers 10 days ago.  Volunteers contributed DNA samples to investigators building a genetic database for study, on condition the data would be deidentified and kept confidential…

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Problem of the Week: A betting puzzle

QUESTION: A gambler playing against the “house” in a game like roulette or slots adopts the rule “Play until you win a certain amount, then stop.”  Will this ensure against player losses? What will be its effect on the house’s profit? ANSWER: Some look at this…

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Problem of the Week: The Second Heads

QUESTION: A friend tosses two coins, and you ask “Is one of them a heads?”  The friend replies “Yes.” What is the probability that the other is a heads? ANSWER:   One-third.  There are four ways the coins could have landed originally: HH:  0.25 probability…

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Problem of the Week: Missing Data

Question: You have a supervised learning task with 30 predictors, in which 5% of the observations are missing.  The missing data are randomly distributed across variables and records. If your strategy for coping with missing data is to drop records with missing data, what proportion…

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