Probability Experiments — Single Events
Grade 5 probability formalizes the fraction representation: the probability of rolling a 3 on a standard die is 1/6 because there is 1 favourable outcome out of 6 equally likely outcomes. This fraction can also be written as a decimal (0.167) or a percent (16.7%). The experimental fraction from many trials should approach this theoretical value. Independence means the previous flip does not change the probability of the next flip: each trial is a fresh start.
Probability as a fraction
P(event) = number of favourable outcomes / total number of equally likely outcomes. P(rolling a 4) = 1/6. P(drawing a red card from a standard deck) = 26/52 = 1/2. P(spinning blue on a spinner with 3 blue sections out of 8) = 3/8. All outcomes must be equally likely for this formula to apply: a bent coin is NOT a fair trial.
Theoretical vs. experimental probability
Theoretical: P(heads) = 1/2 = 0.5 = 50%. Experimental: flip 20 times, get 13 heads. P(heads) = 13/20 = 0.65 = 65%. The experimental differs from theoretical by chance. With 200 flips: might get 103 heads. P = 103/200 = 51.5%. With 2000 flips: even closer to 50%. More trials = closer to theoretical probability.
Independence
Flipping a coin: the first flip is heads. What is P(heads) on the second flip? Still 1/2. The coin has no memory. Each flip is independent: the probability is always 1/2 regardless of previous results. This contradicts the common intuition that tails is due after many heads (the gambler's fallacy). Independence is one of probability's most important and most counter-intuitive ideas.