Probability & Statistics (HS)

Where this is used

Probability and statistics are how you put a number on something you are not sure about, so you can still make a decision. Whenever a field has to deal with uncertainty — approving a new drug from a clinical trial, working out how confident an AI is in its answer, keeping a bank's risk under control — this is the math doing the work underneath.

Key points

Conditional Probability

The probability that A happens, given that you already know B happened. It is what tells a doctor how much a positive test result actually means, and what lets a spam filter judge an email once it has seen the words inside it.

Bayes' Theorem

A rule for updating what you believed before once new evidence arrives. It is the single most important formula here — it is behind an AI deciding whether a photo shows a cat or a dog.

The Normal Distribution

Heights, test scores, measurement errors — a huge number of things in nature pile up around the average μ in a bell shape. About 68% of the values land within μ±σ, and about 95% within μ±2σ. This one shape is the foundation of factory quality control and of financial risk management.

Expected Value

The long-run average of something random — what you would get per try if you repeated it a huge number of times. It is how lotteries, insurance policies and investments are judged.

Hypothesis Testing

A way to ask whether a result is real or just luck — did the drug actually work, or did the numbers happen to fall that way? The p-value answers it: if p < 0.05, the result is called significant, meaning chance alone is a poor explanation. Scientific papers, AI model evaluations and A/B tests use this every single day.

Jobs that use this

Biostatistician (Pharmaceuticals)$135k

Risk Manager (Finance)$160k

Machine Learning Engineer$148k

Probability & Statistics (HS)

Key points

Jobs that use this

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