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A first aid test has two parts, a theory test and a practical test - Edexcel - GCSE Maths - Question 17 - 2022 - Paper 1

Question 17

A first aid test has two parts, a theory test and a practical test. The probability of passing the theory test is 0.75. The probability of passing only one of the tw... show full transcript

Worked Solution & Example Answer:A first aid test has two parts, a theory test and a practical test - Edexcel - GCSE Maths - Question 17 - 2022 - Paper 1

Step 1

Using the given probabilities

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Answer

Let P(T) be the probability of passing the theory test and P(P) be the probability of passing the practical test.

Given:

P(T) = 0.75
P(only one) = 0.36

From the independence of events, the probability of passing only one of the two tests can be represented as:

$P(T) imes (1 - P(P)) + (1 - P(T)) imes P(P) = 0.36$

Step 2

Setting up the equation

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Answer

Substituting the known value of P(T):

$0.75 imes (1 - P(P)) + (1 - 0.75) imes P(P) = 0.36$

This simplifies to:

$0.75 - 0.75P(P) + 0.25P(P) = 0.36$

Combining like terms gives:

$0.75 - 0.50P(P) = 0.36$

Step 3

Solving for the probability of passing the practical test

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Answer

Rearranging the equation:

$-0.50P(P) = 0.36 - 0.75$

This results in:

$-0.50P(P) = -0.39$

Dividing both sides by -0.50:

$P(P) = rac{0.39}{0.50} = 0.78$

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