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…
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…
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…
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?
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…
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…
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…
Question: A baseball team is comparing two of its hitters, Hernandez and Dimock. Hernandez hit .250 in 2017 and .275 in 2018. Dimock did worse in both years - .245 in 2017 and .270 in 2018. Overall, though, Dimock hit better across the two years,…
Question: You work for an internet real-estate company, building statistical models to predict home price on the basis of square footage, number of bedrooms, number of bathrooms, property type (single family home, townhouse, multiplex), and age. Surprisingly, you find the coefficient for bedrooms is negative,…
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…
Your country is at war, and an enemy plane has crashed on your territory. It bears the number 60, and a spy has told you that the aircraft are numbered serially. Can you make a guess about the total number of aircraft the enemy has…
