Bill owns four cars. Each car is a different colour. Each day, he drives to work in one of his cars. The table shows the probability that Bill chooses a car of a particular colour. Car red blue yellow white Probability 0.4 0.17 0.05 Work out the probability that Bill chooses the white car.

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Bill owns four cars - OCR - GCSE Maths - Question 7 - 2017 - Paper 1

Question 7

Bill owns four cars. Each car is a different colour. Each day, he drives to work in one of his cars. The table shows the probability that Bill chooses a car of a par... show full transcript

Worked Solution & Example Answer:Bill owns four cars - OCR - GCSE Maths - Question 7 - 2017 - Paper 1

Step 1

Step 1: Calculate the total probability for all cars

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Answer

To find the probability that Bill chooses the white car, we first need to calculate the total probability of the other cars.

The total probability can be expressed as: $P_{total} = P_{red} + P_{blue} + P_{yellow} + P_{white}$

Using the values from the table: $P_{total} = 0.4 + 0.17 + 0.05 + P_{white}$

Step 2

Step 2: Solve for the probability of the white car

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Answer

Since the total probability must equal 1, we can set up the equation:

$1 = 0.4 + 0.17 + 0.05 + P_{white}$

Calculating the sum of the probabilities for the red, blue, and yellow cars: $0.4 + 0.17 + 0.05 = 0.62$

Now we can solve for the probability of the white car:

$P_{white} = 1 - 0.62 = 0.38$

Thus, the probability that Bill chooses the white car is 0.38.

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