A factory makes 450 pies every day. The pies are chicken pies or steak pies. Each day Milo takes a sample of 15 pies to check. The proportion of the pies in his sample that are chicken is the same as the proportion of the pies made that day that are chicken. On Monday Milo calculated that he needed exactly 4 chicken pies in his sample. (a) Work out the total number of chicken pies that were made on Monday. On Tuesday, the number of steak pies Milo needs in his sample is 6 correct to the nearest whole number. Milo takes at random a pie from the 450 pies made on Tuesday. (b) Work out the lower bound of the probability that the pie is a steak pie.

GCSE Edexcel Maths Ratio Analysis and Problem Solving: A factory makes 450 pies every d

A factory makes 450 pies every day - Edexcel - GCSE Maths - Question 13 - 2017 - Paper 1

Question 13

A factory makes 450 pies every day. The pies are chicken pies or steak pies. Each day Milo takes a sample of 15 pies to check. The proportion of the pies in his sam... show full transcript

Worked Solution & Example Answer:A factory makes 450 pies every day - Edexcel - GCSE Maths - Question 13 - 2017 - Paper 1

Step 1

Work out the total number of chicken pies that were made on Monday.

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Answer

To find the total number of chicken pies made on Monday, we first note that Milo sampled 15 pies and found that 4 were chicken pies.

The proportion of chicken pies in the sample is therefore:

$ext{Proportion} = \frac{4}{15}$

If the total number of pies made is 450, we can find the total number of chicken pies made using the same proportion:

$ext{Total Chicken Pies} = \frac{4}{15} \times 450 = 120$

Thus, the total number of chicken pies made on Monday is 120.

Step 2

Work out the lower bound of the probability that the pie is a steak pie.

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Answer

On Tuesday, the number of steak pies Milo needs in his sample is given as 6, correct to the nearest whole number. Therefore, the actual number of steak pies could range from:

Lower bound: 6 - 0.5 = 5.5,
Upper bound: 6 + 0.5 = 6.5.

Since he takes a sample of 15 pies on Tuesday:

The total number of pies made is still 450. Thus, the possible maximum total number of steak pies on Tuesday can be calculated as:

$450 - 120 = 330$

The lower bound probability of selecting a steak pie is:

$P(\text{steak pie}) = \frac{\text{Lower Bound of Steak Pies}}{\text{Total Number of Pies}} = \frac{330}{450} = \frac{11}{15}$

Hence, the lower bound of the probability that the pie is a steak pie is \frac{11}{15}.

A factory makes 450 pies every day - Edexcel - GCSE Maths - Question 13 - 2017 - Paper 1

Worked Solution & Example Answer:A factory makes 450 pies every day - Edexcel - GCSE Maths - Question 13 - 2017 - Paper 1

Work out the total number of chicken pies that were made on Monday.

Work out the lower bound of the probability that the pie is a steak pie.

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