Probability

Probability measures how likely an event is to occur. It is expressed as a value between 0 (impossible) and 1 (certain), as a fraction, decimal or percentage.

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The Probability Scale

On the scale from 0 to 1: 0 = impossible, 0.5 = equally likely (evens), 1 = certain.

P(event) denotes the probability of an event occurring. P(impossible event) = 0; P(certain event) = 1; P(fair coin shows heads) = 1/2

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Theoretical Probability

When outcomes are equally likely:

P(event) = number of favourable outcomes ÷ total number of outcomes

Example: A fair six-sided die is rolled. P(prime number) = ? Prime numbers on a die: 2, 3, 5 → 3 favourable outcomes out of 6. P(prime) = 3/6 = 1/2

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Complementary Events

P(event does NOT happen) = 1 − P(event)

Example: P(rain tomorrow) = 0.3 → P(no rain) = 1 − 0.3 = 0.7

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Mutually Exclusive Events

Events are mutually exclusive if they cannot both happen at the same time.

For mutually exclusive events A and B: P(A or B) = P(A) + P(B)

Example: Rolling a die: P(2 or 5) = 1/6 + 1/6 = 1/3