A collection of the exercises from the advanced probability chapter, in order of appearance in the book: conditional probability and Bayes’ theorem, diagnostic tests, game theory and expected value, the three representations (contingency table, tree, Venn), combinatorics, the binomial scheme, betting and fair games, and finally descriptive statistics, surveys and classic paradoxes. The worked exercises give the complete solution; the final problems (statistics and paradoxes) provide the setup and the method, leaving the calculation to the student.
- Two red balls without replacement
- Sum of at least 9 with the first die even
- Overweight person and sport (Bayes)
- At least one head in three tosses
- Diagnostic test with 10% prevalence
- Independent or mutually exclusive
- Bicycle or scooter
- Precision with 2% prevalence
- Lottery and risk aversion
- Matrix with a dominant strategy
- Rock-paper-scissors, mixed equilibrium
- Variant of odds or evens
- Prepared student and correct answer
- Three green balls without replacement
- Vaccinated and ill
- Anagrams of PRECIPITEVOLISSIMEVOLMENTE
- Ice-cream cups with repetition
- Four-letter password
- Rows of boys and girls
- Five-card hands from 32
- The 6 twice in six rolls
- At least one head in four tosses
- Defective items in a batch
- Odds of 2,5 to 1 and the margin
- Die with winnings and losses
- Mean, median, variance, standard deviation
- Confidence interval for light bulbs
- Sample size for a 1% error
- Margin of error and representativeness
- Simulating Monty Hall with a die
- Monty Fall variant
- Paradox of the two children born on a Tuesday
- Bertrand’s three answers
- Essential solutions — further exercises