Probability

Japanese school year: Math A

What you learn

Learn the fundamental rules of probability to quantify how likely an event is to occur among all equally likely outcomes. Probability is indispensable for risk assessment, statistical decision-making, and analyzing games of chance. Mastering prior counting techniques like permutations and combinations will prepare you well for calculating probabilities accurately.

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Key points

This formula finds the probability of event $A$ when all outcomes are equally likely. It divides the number of favorable outcomes $n(A)$ by the total number of possible outcomes $n(U)$ .

P(A) = \frac{n(A)}{n(U)}

This addition rule calculates the probability that event $A$ or event $B$ occurs. It adds the individual probabilities $P(A)$ and $P(B)$ , then subtracts the overlap $P(A \cap B)$ counted twice.

P(A \cup B) = P(A) + P(B) - P(A \cap B)

This formula finds the probability that event $A$ does not occur (the complement rule). For problems asking for 'at least once,' subtracting the chance of never happening from 1 is much easier.

P(\bar{A}) = 1 - P(A)

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Practice 1Coming soon