In a survey, 60 students were asked whether they have a bank account (B) and whether they have a part-time job (J). The number of students who had neither a bank account nor a part-time job was $x$. The Venn diagram shows the results in terms of $x$. One of the 60 students is chosen at random. Find the probability that they have a bank account. Show your working.

GCSE OCR Maths Constructions: In a survey, 60 students were as

In a survey, 60 students were asked whether they have a bank account (B) and whether they have a part-time job (J) - OCR - GCSE Maths - Question 4 - 2020 - Paper 1

Question 4

In a survey, 60 students were asked whether they have a bank account (B) and whether they have a part-time job (J). The number of students who had neither a bank ac... show full transcript

Worked Solution & Example Answer:In a survey, 60 students were asked whether they have a bank account (B) and whether they have a part-time job (J) - OCR - GCSE Maths - Question 4 - 2020 - Paper 1

Step 1

Find the total number of students with a bank account and a part-time job.

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Answer

From the Venn diagram:

Students with only a bank account = $2x$ .
Students with only a part-time job = $5 - 2$ .
Students with both = $x - 1$ .

The total number of students can be expressed as: $2x + (x - 1) + (5 - 2) + x = 60.$

Step 2

Solve for x.

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Answer

Collecting like terms gives: $4x + 2 = 60.$ Subtracting 2 from both sides: $4x = 58.$ Dividing by 4: $x = rac{58}{4} = 14.5.$

Step 3

Calculate the number of students with a bank account.

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Answer

Substituting $x = 14.5$ back into the expressions:

Students with a bank account = $2x + (x - 1)$
This is equal to: $2(14.5) + (14.5 - 1) = 29 + 13.5 = 42.5.$

Step 4

Determine the probability of choosing a student with a bank account.

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Answer

The probability of a student having a bank account is calculated by dividing the number of students with a bank account by the total number of students: $ext{Probability}= \frac{42.5}{60} = \frac{85}{120} = \frac{17}{24}.$ Thus, the probability that the chosen student has a bank account is (\frac{17}{24}).

In a survey, 60 students were asked whether they have a bank account (B) and whether they have a part-time job (J) - OCR - GCSE Maths - Question 4 - 2020 - Paper 1

Worked Solution & Example Answer:In a survey, 60 students were asked whether they have a bank account (B) and whether they have a part-time job (J) - OCR - GCSE Maths - Question 4 - 2020 - Paper 1

Find the total number of students with a bank account and a part-time job.

Solve for x.

Calculate the number of students with a bank account.

Determine the probability of choosing a student with a bank account.

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