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There are $p$ counters in a bag - Edexcel - GCSE Maths - Question 13 - 2019 - Paper 1

Question 13

There are $p$ counters in a bag. 12 of the counters are yellow. Shafiq takes at random 30 counters from the bag. 5 of these 30 counters are yellow. Work out an est... show full transcript

Worked Solution & Example Answer:There are $p$ counters in a bag - Edexcel - GCSE Maths - Question 13 - 2019 - Paper 1

Step 1

Estimate the proportion of yellow counters from the sample

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Answer

In Shafiq's sample of 30 counters, 5 are yellow. Therefore, the proportion of yellow counters in this sample can be calculated as:

$ext{Proportion of yellow counters} = \frac{5}{30} = \frac{1}{6}$

Step 2

Set up the equation to find the total number of counters, $p$

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Answer

Since we know that 12 out of the total $p$ counters are yellow, we can set up the equation based on the proportion:

$\frac{12}{p} = \frac{1}{6}$

Step 3

Solve the equation for $p$

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Answer

Cross-multiplying gives:

$12 \times 6 = 1 \times p \\ p = 72$

Thus, the estimated value of $p$ is approximately 72.

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