Card 1Uncertainty, Sample Spaces, and Events
HintThink of it as a scale from impossible to certain.Memory Tip0 = no chance, 1 = sure thing.
Card 2Uncertainty, Sample Spaces, and Events
HintIt's the 'experiment' that produces an outcome.Memory TipThink 'random experiment'.
Card 3Uncertainty, Sample Spaces, and Events
HintIt's the 'universe' of outcomes.Memory TipSample = list of all possibilities.
Card 4Uncertainty, Sample Spaces, and Events
HintIt's a subset of the sample space.Memory TipAn event is a 'group of outcomes'.
Card 5Uncertainty, Sample Spaces, and Events
HintIt's a simple fraction: what you want over what's possible.Memory TipCount favorable / total.
Card 6Uncertainty, Sample Spaces, and Events
HintIt's the opposite of event A.Memory TipComplement = 'everything else'.
Card 7Uncertainty, Sample Spaces, and Events
HintIt's a simple subtraction from 1.Memory Tip1 minus the probability of A.
Card 8Uncertainty, Sample Spaces, and Events
HintThey have no outcomes in common.Memory TipMutually exclusive = no overlap.
Card 9Uncertainty, Sample Spaces, and Events
HintAdd probabilities, then subtract the overlap if there is one.Memory TipAdd, then subtract double-count.
Card 10Uncertainty, Sample Spaces, and Events
HintIt's like counting items in two groups twice.Memory TipDon't double-count the overlap.
Card 11Uncertainty, Sample Spaces, and Events
HintEven numbers on a die are 2, 4, and 6.Memory Tip3 evens out of 6 sides = 1/2.
Card 12Uncertainty, Sample Spaces, and Events
HintUse the complement rule: 1 minus the probability all work.Memory Tip1 - (0.99)^10.
Card 13Uncertainty, Sample Spaces, and Events
HintIt's a fallacy about independence.Memory TipThe coin has no memory.
Card 14Uncertainty, Sample Spaces, and Events
HintIt's not the same as the gambler's fallacy.Memory TipExtreme followed by less extreme.
Card 15Uncertainty, Sample Spaces, and Events
HintBigger samples give more stable estimates.Memory TipLarge samples converge to the truth.
Card 16Uncertainty, Sample Spaces, and Events
HintIt's a 'hidden' variable that confuses the relationship.Memory TipConfounder = third variable.
Card 17Uncertainty, Sample Spaces, and Events
HintIt's a ratio, not an absolute number.Memory TipRelative = proportion reduction.
Card 18Uncertainty, Sample Spaces, and Events
HintIt's the simple difference in probabilities.Memory TipAbsolute = simple difference.
Card 19Uncertainty, Sample Spaces, and Events
HintAssociation is not causation.Memory TipCorrelation ≠ causation.
Card 20Uncertainty, Sample Spaces, and Events
HintSize alone does not guarantee accuracy.Memory TipBig but biased = confidently wrong.
Card 21Conditional Probability and Independence
HintIt updates probability based on new information.Memory TipP(A given B) = P(A and B) / P(B).
Card 22Conditional Probability and Independence
HintIt's the probability of both divided by the probability of the condition.Memory TipJoint probability divided by marginal.
Card 23Conditional Probability and Independence
HintP(A | B) = P(A) and P(A and B) = P(A)P(B).Memory TipNo influence between events.
Card 24Conditional Probability and Independence
HintMutually exclusive events are dependent by definition.Memory TipMutually exclusive = dependent.
Card 25Conditional Probability and Independence
HintIt's the probability of both events happening.Memory TipMultiply, using conditional if needed.
Card 26Conditional Probability and Independence
HintIt helps update beliefs based on evidence.Memory TipBayes flips the condition.
Card 27Conditional Probability and Independence
HintIt's the prior probability before any test.Memory TipBase rate = starting point.
Card 28Conditional Probability and Independence
HintIt's a 'false alarm'.Memory TipFalse positive = false alarm.
Card 29Conditional Probability and Independence
HintIt's a 'miss'.Memory TipFalse negative = missed detection.
Card 30Conditional Probability and Independence
HintIt's the positive predictive value.Memory TipP(condition | positive).
Card 31Conditional Probability and Independence
HintMost positive tests are false positives when the condition is rare.Memory Tip95 true positives / 590 total positives.
Card 32Conditional Probability and Independence
HintUse the conditional probability formula.Memory Tip25/40 = 0.625.
Card 33Conditional Probability and Independence
HintIt's the intersection of the two events.Memory Tip25/100 = 0.25.
Card 34Conditional Probability and Independence
HintIt's a simple proportion.Memory Tip60/100 = 0.6.
Card 35Random Variables, Expected Value, and Variation
HintIt turns random outcomes into numbers.Memory TipRandom variable = number from chance.
Card 36Random Variables, Expected Value, and Variation
HintThink 'countable' values.Memory TipDiscrete = countable.
Card 37Random Variables, Expected Value, and Variation
HintThink 'measured' values.Memory TipContinuous = measured on a scale.
Card 38Random Variables, Expected Value, and Variation
HintIt's a 'map' of probabilities for each value.Memory TipProbabilities sum to 1.
Card 39Random Variables, Expected Value, and Variation
HintIt's a weighted average of all possible outcomes.Memory TipSum of (value * probability).
Card 40Random Variables, Expected Value, and Variation
HintMultiply each payout by its probability and add.Memory Tip10*0.2 + 0*0.8 = $2.
Card 41Random Variables, Expected Value, and Variation
HintIt quantifies how much values vary.Memory TipAverage of squared differences from mean.
Card 42Random Variables, Expected Value, and Variation
HintIt's the 'typical' distance from the mean.Memory TipSquare root of variance.
Card 43Random Variables, Expected Value, and Variation
HintThink 'number of heads in 20 coin flips'.Memory TipBINS: Binary, Independent, Number fixed, Same p.
Card 44Random Variables, Expected Value, and Variation
HintIt's a mnemonic for the conditions of a binomial setting.Memory TipBINS = conditions for binomial.
Card 45Random Variables, Expected Value, and Variation
HintIt's the classic 'bell curve'.Memory TipBell curve = normal distribution.
Card 46Random Variables, Expected Value, and Variation
HintIt's a rule of thumb for the spread of normal data.Memory Tip68-95-99.7 rule.
Card 47Random Variables, Expected Value, and Variation
HintEach flip is independent with a 50% chance of heads.Memory TipBinomial with n=20, p=0.5.
Card 48Random Variables, Expected Value, and Variation
HintSubtract the cost from the expected payout.Memory Tip$2 - $3 = -$1.
Card 49Random Variables, Expected Value, and Variation
HintMultiply each outcome (1-6) by its probability (1/6) and sum.Memory Tip(1+2+3+4+5+6)/6 = 3.5.
Card 50Random Variables, Expected Value, and Variation
HintCalculate the average squared deviation from the mean of 3.5.Memory TipAbout 2.92.
Card 51Random Variables, Expected Value, and Variation
HintIt's the square root of the variance.Memory TipAbout 1.71.
Card 52Random Variables, Expected Value, and Variation
HintUse the binomial formula with n=20, p=0.5, k=10.Memory TipAbout 0.176.
Card 53Random Variables, Expected Value, and Variation
HintSum the probabilities of 0, 1, and 2 heads.Memory TipAbout 0.5.
Card 54Random Variables, Expected Value, and Variation
HintUse the empirical rule.Memory TipAbout 5% (100% - 95%).
Card 55Random Variables, Expected Value, and Variation
HintUse the empirical rule.Memory TipAbout 68%.
Card 56Probability Traps and Real-World Reasoning
HintThink of a gambler watching a roulette wheel that has landed on black many times in a row.Memory TipThe coin has no memory.
Card 57Probability Traps and Real-World Reasoning
HintThink of a student who scores exceptionally high on one test and then scores closer to their average on the next.Memory TipExtreme goes back to average.
Card 58Probability Traps and Real-World Reasoning
HintThink of flipping a coin 10 times vs. 1000 times.Memory TipMore data, more stable.
Card 59Probability Traps and Real-World Reasoning
HintThink of ice cream sales and drowning incidents both rising in summer.Memory TipThe hidden third factor.
Card 60Probability Traps and Real-World Reasoning
HintThink of a headline saying a drug cuts heart attack risk by half.Memory TipProportion of original risk.
Card 61Probability Traps and Real-World Reasoning
HintThink of the actual number of people affected per 10,000.Memory TipThe real number change.
Card 62Probability Traps and Real-World Reasoning
HintThink of the classic example of stork populations and birth rates.Memory TipAssociation is not causation.
Card 63Probability Traps and Real-World Reasoning
HintThink of a political poll that only calls landline phones.Memory TipBig but biased.
Card 64Probability Traps and Real-World Reasoning
HintThink of all the numbers on a die.Memory TipThe universe of outcomes.
Card 65Probability Traps and Real-World Reasoning
HintThink of narrowing the group you are looking at.Memory TipProbability given new info.
Card 66Probability Traps and Real-World Reasoning
HintThink of interpreting a medical test result.Memory TipReverse the conditional.
Card 67Probability Traps and Real-World Reasoning
HintThink of how common a disease is in the general population.Memory TipThe starting prevalence.
Card 68Probability Traps and Real-World Reasoning
HintThink of the average payout of a game over many plays.Memory TipLong-run average.
Card 69Probability Traps and Real-World Reasoning
HintThink of how spread out the data are from the mean.Memory TipSpread from the mean.
Card 70Probability Traps and Real-World Reasoning
HintThink of counting heads in a set number of coin flips.Memory TipBINS: Binary, Independent, Number fixed, Same p.
Card 71Probability Traps and Real-World Reasoning
HintThink of height or test score distributions.Memory TipBell curve.
Card 72Probability Traps and Real-World Reasoning
HintThink of the percentages 68, 95, 99.7.Memory Tip68-95-99.7 rule.
Card 73Probability Traps and Real-World Reasoning
HintThink of rolling a 2 and a 5 on a single die roll.Memory TipCannot both occur.
Card 74Probability Traps and Real-World Reasoning
HintThink of coin flips: the result of one flip does not affect the next.Memory TipNo influence between events.
Card 75Probability Traps and Real-World Reasoning
HintThink of the chance it does not rain.Memory Tip1 minus P(A).