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AQA GCSE · Question 20.1 · Probability
Beth and Lynn each spin the same biased coin a number of times. The table shows information about the results. How many more Heads did Beth spin than Lynn?
Beth and Lynn each spin the same biased coin a number of times. The table shows information about the results. How many more Heads did Beth spin than Lynn?
How to approach this question
1. Recall the formula for relative frequency: Relative Frequency = (Number of successful outcomes) / (Total number of trials).
2. Rearrange the formula to find the number of heads: Number of Heads = Relative Frequency × Number of spins.
3. Calculate the number of heads for Beth: 0.32 × 125.
4. Calculate the number of heads for Lynn: 0.35 × 80.
5. Find the difference between the number of heads Beth got and the number of heads Lynn got.
Full Answer
The number of times an event happens can be calculated from its relative frequency and the total number of trials using the formula:
Number of outcomes = Relative frequency × Total trials
For Beth:
Number of Heads = Relative frequency of Heads × Number of spins
Number of Heads for Beth = 0.32 × 125 = 40
For Lynn:
Number of Heads = Relative frequency of Heads × Number of spins
Number of Heads for Lynn = 0.35 × 80 = 28
The question asks how many *more* Heads Beth spun than Lynn.
Difference = Beth's Heads - Lynn's Heads
Difference = 40 - 28 = 12.
Beth spun 12 more Heads than Lynn.
Common mistakes
✗ Dividing by the relative frequency instead of multiplying.
✗ Calculating the number of tails instead of heads.
✗ Subtracting the relative frequencies or the number of spins directly.
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