Theoretical and experimental probability

Experimental probability = event occurrences / trial count. With many independent trials under the same conditions, relative frequency generally approaches theoretical probability but can fluctuate.

Add event occurrences from both series, then add their trial counts. Divide total occurrences by total trials. The simple average of the two frequencies is unsuitable when the series lengths differ.

Expected occurrences = trial count × event probability. For p%, use n × p/100. This is an expected average, not a guarantee.

Each independent fair-coin toss has heads probability 1/2. The probability of heads on all n tosses is (1/2)ⁿ. Multiply the probabilities rather than adding.

Calculate red then blue and blue then red separately. The total number of available balls decreases for the second draw. The two cases are disjoint, so add their probabilities.

Complement probability = 1 − P(A), or 100% − p% in percentages. In the finite models used here, 0 denotes an impossible event and 1 a certain event.

Select the table columns satisfying the event and add their frequencies. Divide by the sum of all frequencies. For the theoretical probability, count favourable faces out of six equally likely faces. Subtract the theoretical probability from the empirical one and check the sign.

Complement probability = 1 − P(A), or 100% − p% in percentages. In the finite models used here, 0 denotes an impossible event and 1 a certain event.

Experimental probability = event occurrences / trial count. With many independent trials under the same conditions, relative frequency generally approaches theoretical probability but can fluctuate.

A fair die has six equally likely outcomes. Count outcomes from 1 through n and divide by 6. For 1 ≤ n ≤ 6, the probability is n/6.