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Probability basics

Probability

Japanese school year: Junior high 2

What you learn

You will learn how to determine the probability of an event when all outcomes are equally likely. This concept is fundamental for analyzing uncertainty, predicting game odds, and making risk assessments. Being able to count outcomes systematically without omission or duplication beforehand is highly beneficial.

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Key points

This is the fundamental formula to calculate the probability P(A)P(A) of an event AA, assuming all outcomes are equally likely. Divide the favorable cases n(A)n(A) by the total possible cases n(U)n(U).

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

This shows the possible range of values for probability P(A)P(A). It is always between 0 and 1, taking 0 for an impossible event and 1 for a certain event.

0≤P(A)≤10 \le P(A) \le 1

Use this formula to find the probability that event AA does not occur (the complement). Simply subtract the probability of AA occurring, P(A)P(A), from the total probability 1.

P(Aˉ)=1−P(A)P(\bar{A}) = 1 - P(A)

This formula finds the probability that either event AA or BB occurs. If AA and BB cannot happen at the same time (mutually exclusive), simply add their probabilities together.

P(A∪B)=P(A)+P(B)(A∩B=∅)P(A \cup B) = P(A) + P(B) \quad (A \cap B = \emptyset)

Choose a set to practice.