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When a drawing pin is dropped it can land point down or point up - Edexcel - GCSE Maths - Question 8 - 2017 - Paper 3
Question 8
When a drawing pin is dropped it can land point down or point up. Lucy, Mel and Tom each dropped the drawing pin a number of times. The table shows the number of ti... show full transcript
Worked Solution & Example Answer:When a drawing pin is dropped it can land point down or point up - Edexcel - GCSE Maths - Question 8 - 2017 - Paper 3
Step 1
Whose results will give the best estimate for the probability that the drawing pin will land point up?
Answer
To determine whose results provide the best estimate for the probability of the drawing pin landing point up, we calculate the respective probabilities for Lucy, Mel, and Tom.
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For Lucy:
- Total Drops = 31 (down) + 14 (up) = 45
- Probability (up) = ( \frac{14}{45} )
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For Mel:
- Total Drops = 53 (down) + 27 (up) = 80
- Probability (up) = ( \frac{27}{80} )
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For Tom:
- Total Drops = 16 (down) + 9 (up) = 25
- Probability (up) = ( \frac{9}{25} )
Next, we simplify these probabilities:
- Lucy: ( \frac{14}{45} \approx 0.3111 )
- Mel: ( \frac{27}{80} = 0.3375 )
- Tom: ( \frac{9}{25} = 0.36 )
Tom's probability of ( 0.36 ) is the highest, making his results the best estimate for the probability that the drawing pin will land point up.
Step 2
Use all the results in the table to work out an estimate for the probability that the drawing pin will land point up the first time and point down the second time.
Answer
To find the probability that the drawing pin will land point up the first time and point down the second time, we need to calculate the individual probabilities using the total number of throws for each outcome.
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Calculate total number of throws for point up and point down:
- Total point down = 31 + 53 + 16 = 100
- Total point up = 14 + 27 + 9 = 50
- Overall total = 100 + 50 = 150
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Calculate probabilities:
- Probability (up) = ( \frac{50}{150} = \frac{1}{3} )
- Probability (down) = ( \frac{100}{150} = \frac{2}{3} )
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Combine probabilities for both events:
- Probability (up first, down second) = Probability (up) × Probability (down)
- = ( \frac{1}{3} \times \frac{2}{3} = \frac{2}{9} )
So the estimated probability that the drawing pin will land point up the first time and point down the second time is ( \frac{2}{9} ).