What is the Conjunction Fallacy? The conjunction fallacy is a cognitive bias that occurs when someone mistakenly believes that two events occurring together are more likely than either of the two events alone. In other words, it’s the mistaken belief that a precisely detailed, multifaced outcome is more likely to occur than a more generalized […] The post Conjunction Fallacy: Definition & Example appeared first on Statistics By Jim ..read more

What is Base Rate Fallacy? Base rate fallacy is a cognitive bias that occurs when a person misjudges an outcome by giving too much weight to case-specific details and overlooks crucial probability information that applies to all cases in a population. That vital probability is the outcome’s base rate of occurrence in the population. In […] The post Base Rate Fallacy Overview & Examples appeared first on Statistics By Jim ..read more

What’s the risk? People discuss risk frequently, but it’s not always clearly understood. It is your exposure to danger or adverse outcomes. Statistically, we define risk as the probability of a negative outcome occurring, and there are several ways to calculate it. Imagine deciding whether to take a medication to reduce the chances of an […] The post Risk Calculations: Relative vs Absolute & Risk Reduction appeared first on Statistics By Jim ..read more

Binomial Distribution Formula Use the binomial distribution formula to calculate the likelihood an event will occur a specific number of times in a set number of opportunities. I’ll show you the binomial distribution formula to calculate these probabilities manually. In this post, I’ll walk you through the formulas for how to find the probability, mean, […] The post Binomial Distribution Formula: Probability, Standard Deviation & Mean appeared first on Statistics By Jim ..read more

What is the Expected Value? The expected value in statistics is the long-run average outcome of a random variable based on its possible outcomes and their respective probabilities. Essentially, if an experiment (like rolling a dice or a game of chance) were repeated indefinitely, the expected value tells us the average result we’d see in […] The post Expected Value: Definition, Formula & Finding appeared first on Statistics By Jim ..read more

What is the Bernoulli Distribution? The Bernoulli distribution is a discrete probability distribution that models a binary outcome for one trial. Use it for a random variable that can take one of two outcomes: success (k = 1) or failure (k = 0), much like a coin toss. Statisticians refer to these trials as Bernoulli […] The post Bernoulli Distribution: Uses, Formula & Example appeared first on Statistics By Jim ..read more

What is Joint Probability? Joint probability is the likelihood that two or more events will coincide. Knowing how to calculate them allows you to solve problems such as the following. What is the probability of: Getting two heads in two coin tosses? Consecutively drawing two aces from a deck of cards? The next customer being […] The post Joint Probability: Definition, Formula & Examples appeared first on Statistics By Jim ..read more

What are Independent Events? Independent events in statistics are those in which one event does not affect the next event. More specifically, the occurrence of one event does not affect the probability of the following event happening. Here are three quick examples of independent events: Flipping a coin. The outcome of one coin toss has […] The post Independent Events: Definition & Probability appeared first on Statistics By Jim ..read more

What is a Probability Mass Function? A probability mass function (PMF) is a mathematical function that calculates the probability a discrete random variable will be a specific value. PMFs also describe the probability distribution for the full range of values for a discrete variable. A discrete random variable can take on a finite or countably […] The post Probability Mass Function: Definition, Uses & Example appeared first on Statistics By Jim ..read more

What is a Cumulative Distribution Function? A cumulative distribution function (CDF) describes the probabilities of a random variable having values less than or equal to x. It is a cumulative function because it sums the total likelihood up to that point. Its output always ranges between 0 and 1. CDFs have the following definition: CDF(x) […] The post Cumulative Distribution Function (CDF): Uses, Graphs & vs PDF appeared first on Statistics By Jim ..read more