Randomness and probability: basic calculations

A die has 6 sides. The probability of rolling a six is 1 out of 6. The probability of rolling an even number (2, 4, 6) is 3 out of 6 — that is, half.

The rule: Count how many outcomes are favourable to you, and divide by the total number of outcomes available.

A coin: 1 out of 2. A bag with 3 red and 2 blue balls: the probability of red is 3 out of 5.

Computer programs use random functions to generate varied results. AI models use randomness when selecting the next word in a text, which is why answers can vary when questions are repeated.

Test the hypothesis: Roll a die 30 times and count the number of sixes. You expect roughly 5. Did you get 3? 8? Randomness does not yield the exact expected value with few observations. But with 300 rolls, the result will be closer to 50 than 30 rolls are to 5.

Two dice: The sum 7 can be achieved in six ways (1+6, 2+5, 3+4, 4+3, 5+2, 6+1) out of 36 possible combinations. The sum 2 can only be achieved in one way (1+1). Therefore, 7 is the most common sum.