Mathematics from zero
Probability: free-recall review
Recall is harder than re-reading, and that difficulty is exactly what makes it stick. For each prompt, say or write a full answer from memory before you open the model answer — then check what you missed.
Reconstruct the unit’s core ideas from memory — what a probability is, the 0-to-1 scale, favourable over total, when to multiply versus add, and the complement — without looking back at the lessons.
- 01What does a probability measure, and what does the 0-to-1 scale mean?
- 02For equally likely outcomes, how do you compute the probability of an event, and why can it never exceed 1?
- 03What does it mean for two events to be independent, and give one example of dependent events?
- 04When two events are independent, how do you find the probability that both happen, and why does the result get smaller?
- 05When do you add probabilities instead of multiplying, and what condition must hold?
- 06What is the complement of an event, and how do you compute it?
If you could rebuild each answer from memory, you hold the unit’s spine: a probability is a number from 0 to 1, favourable over total for equally likely outcomes; independence is whether one result changes the other’s possibilities; both independent events happening multiplies; either of two exclusive events happening adds; and an event not happening is 1 minus its probability. The hard part is never the arithmetic — it is matching the operation to the question.