Why this matters
Every survey, experiment and model you build rests on probability. If you understand how random variation behaves, you can tell a lender whether a jump in defaults is alarming or normal, and tell an NGO why 400 households can say something useful about a district of thousands.
Probability in one paragraph
A probability is a number from 0 to 1 describing how likely something is. If 3 in every 10 maize farmers in a cooperative grow soya too, the probability that a randomly chosen member grows soya is 0.3. Two rules carry you a long way. The chance that something does not happen is 1 minus the chance it does. And for independent events, the chance that both happen is the product: two randomly chosen members both growing soya has probability 0.3 × 0.3 = 0.09.
Distributions: the shape of variation
A distribution describes which values a variable takes and how often. Three shapes appear constantly.
- Binomial: counts of yes or no outcomes, such as how many of 20 borrowers repay on time.
- Normal: the symmetric bell shape, common for measurements like heights, and central to inference.
- Skewed: most values small with a long tail of large ones, typical of incomes, mobile money transaction amounts and farm sizes.
For skewed data the mean is pulled up by the tail, so the median often describes a typical value better. Always plot a histogram before choosing a summary.