Relative frequency estimates probability from data: successful outcomes divided by trials. With more independent repetitions under the same conditions, it often settles towards the underlying probability, but short runs can fluctuate. Example A spinner lands on blue 84 times in 200 trials. Its experimental estimate is 84/200=0.42. In 500 similar spins, an expected blue count is 500(0.42)=210. Expected frequency equals number of trials times probability. It describes a long-run average, not a guaranteed count in one experiment. A small sample giving an unusual result is not by itself proof of an unfair device. A fair device gives outcomes according to the stated equal-chance model. Bias favours some outcomes. Random selection uses chance so the chosen result is not deliberately determined.

Relative frequency estimates probability from data: successful outcomes divided by trials. With more independent repetitions under the same conditions, it often settles towards the underlying probability, but short runs can fluctuate.

A spinner lands on blue 84 times in 200 trials. Its experimental estimate is \(84/200=0.42\). In 500 similar spins, an expected blue count is \(500(0.42)=210\).

Expected frequency equals number of trials times probability. It describes a long-run average, not a guaranteed count in one experiment. A small sample giving an unusual result is not by itself proof of an unfair device.

A fair device gives outcomes according to the stated equal-chance model. Bias favours some outcomes. Random selection uses chance so the chosen result is not deliberately determined.

Probability

Cambridge IGCSE Mathematics 0580. Initial catalogue covers the assessed demands of February/March 2026 Paper 22; further Core and Extended mappings require paper-level scope review.

Experiments, estimates and expected counts

Experiments, estimates and expected counts