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AQA GCSE · Question 07.1 · Probability
Beth and Lynn each spin the same biased coin a number of times. The table shows information about the results.
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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.
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<br>
How many more Heads did Beth spin than Lynn?
How to approach this question
1. Recall the formula: Relative Frequency = (Number of successful outcomes) / (Total number of trials).
2. Rearrange it to find the number of Heads for Beth: Number of Heads = Relative Frequency × Number of spins.
3. Calculate the number of Heads for Beth.
4. Calculate the number of Heads for Lynn using the same method.
5. Find the difference between the number of Heads Beth spun and the number Lynn spun.
Full Answer
**Step 1: Calculate the number of Heads for Beth.**
Number of Heads = Relative frequency of Heads × Number of spins
Beth's Heads = 0.32 × 125 = 40
**Step 2: Calculate the number of Heads for Lynn.**
Lynn's Heads = 0.35 × 80 = 28
**Step 3: Find the difference.**
Difference = Beth's Heads - Lynn's Heads
Difference = 40 - 28 = 12
**Answer: 12**
The formula for relative frequency is:
Relative Frequency = Number of Heads / Number of spins
To find the number of heads, we can rearrange this:
Number of Heads = Relative Frequency × Number of spins
For Beth:
Number of Heads = 0.32 × 125 = 40
For Lynn:
Number of Heads = 0.35 × 80 = 28
The question asks how many *more* Heads Beth spun than Lynn.
Difference = 40 - 28 = 12.
Common mistakes
✗ Subtracting the relative frequencies (0.35 - 0.32).
✗ Subtracting the number of spins (125 - 80).
✗ Calculating the number of heads for each person correctly but then failing to find the difference.
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