Probability and probability distributions are the language of uncertainty. This lesson explains basic probability concepts, conditional probability and Bayes’ theorem, common probability distributions, and why they matter for business analytics.
Business decisions often involve uncertainty: will a campaign convert, will a machine fail, how many customers will churn? Probability gives a structured way to quantify uncertainty and make decisions under risk. Distributions describe how likely different outcomes are and are the backbone of forecasting, risk modelling, and A/B testing.
Probability of an event is a number between 0 and 1 representing its likelihood. Key rules:
If a campaign has a 0.2 probability of conversion, expected conversions from 1,000 impressions = 0.2 × 1,000 = 200.
Conditional probability P(B|A) is the probability of B given A occurred. Bayes’ theorem updates beliefs when new evidence arrives:
Bayes’ Theorem: P(A|B) = [P(B|A) × P(A)] / P(B)
A fraud detection model shows a transaction is flagged (B). Using Bayes’ theorem, a bank updates the probability that the transaction is actually fraudulent (A) given the flag and historical fraud rates.
Describes number of successes in n independent trials with probability p.
Use-case: number of conversions in 100 email sends.
Mean: n·p • Var: n·p·(1−p)
Models count of events over fixed interval (rare events).
Use-case: number of calls to support per hour.
Mean = Var = λ (rate)
Bell-shaped distribution; many natural measures approximate normal.
Use-case: measurement errors, heights, process variation.
Mean = μ • Std Dev = σ
Models time between independent events.
Use-case: time until next website visit or time-to-failure for some equipment.
Mean = 1/λ • Var = 1/λ²
All outcomes equally likely.
Use-case: simple simulations, baseline comparisons.
A call center receives on average 12 calls per hour. Which distribution fits count of calls per hour? Estimate the mean and variance. Explain how you would use this to staff agents.