Relative and Expected Frequencies (Copy)

Cheat Sheet: Relative Frequency and Expected Frequencies (IGCSE Mathematics 0580 – CORE)
Topic: Experimental Probability, Expected Value, Fairness, Bias, and Randomness

1. Relative Frequency

• Relative frequency is used to estimate the probability of an event based on experimental results.
• Formula:

Relative Frequency=Number of times event occursTotal number of trialstext{Relative Frequency} = frac{text{Number of times event occurs}}{text{Total number of trials}}

• As the number of trials increases, the relative frequency becomes a better estimate of the true probability.

2. Expected Frequency

• Expected frequency is how often you expect an event to happen based on probability and number of trials.
• Formula:

Expected Frequency=Probability×Total number of trialstext{Expected Frequency} = text{Probability} times text{Total number of trials}

• You can use experimental probability (relative frequency) or theoretical probability to calculate expected frequency.

3. Understanding Fair, Bias, and Random

4. Examples

• Relative Frequency Example:
  A spinner is spun 100 times. It lands on red 25 times.
  Estimated probability of red = 25 ÷ 100 = 0.25.
• Expected Frequency Example:
  If probability of getting red is 0.25 and you spin the spinner 200 times:
  Expected number of reds = 0.25 × 200 = 50.

5. Important Tips

• Relative frequency is based on actual results, not theoretical assumptions.
• Expected frequency is an estimate — actual results may differ.
• Always check if a situation describes a fair or biased setup.
• Random experiments (like tossing a fair coin) mean each outcome is equally likely without prediction.

This cheat sheet fully covers all CORE-level concepts for understanding relative frequency, calculating expected frequencies, and identifying fairness, bias, and randomness.