Over a long period of time, it is found that the probability of a train from Bewford to London being late is 0.2. (i) One morning there are two trains from Bewford to London. Use the information to complete the tree diagram. First train Late Not late Second train Late Not late (ii) Work out the probability that both trains are not late. (iii) Give a reason why the probabilities used in the tree diagram for the second train may not be reliable.

GCSE OCR Maths Probability: Over a long period of time, it i

Over a long period of time, it is found that the probability of a train from Bewford to London being late is 0.2 - OCR - GCSE Maths - Question 7 - 2021 - Paper 1

Question 7

Over a long period of time, it is found that the probability of a train from Bewford to London being late is 0.2. (i) One morning there are two trains from Bewford ... show full transcript

Worked Solution & Example Answer:Over a long period of time, it is found that the probability of a train from Bewford to London being late is 0.2 - OCR - GCSE Maths - Question 7 - 2021 - Paper 1

Step 1

i) Complete the tree diagram.

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Answer

On the left branch for the first train:

Probability that the first train is late: 0.2
Probability that the first train is not late: 0.8 (since 1 - 0.2 = 0.8)

On the right branch for the second train:

The probability structure for the second train is assumed to be the same as the first train for simplicity (unless otherwise specified).

Probability that the second train is late: 0.2
Probability that the second train is not late: 0.8.

Step 2

ii) Work out the probability that both trains are not late.

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Answer

To find the probability that both trains are not late, we multiply their individual probabilities of being not late:

$P( ext{Both not late}) = P( ext{First not late}) imes P( ext{Second not late})$

This gives:

$P( ext{Both not late}) = 0.8 imes 0.8 = 0.64$

Thus, the probability that both trains are not late is 0.64.

Step 3

iii) Give a reason why the probabilities used in the tree diagram for the second train may not be reliable.

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Answer

The probabilities for the second train may not be reliable because they are based on historical data from the first train. External factors such as weather conditions, operational issues, or schedules may cause the probabilities to differ for each train. Therefore, assuming the same probabilities without accounting for these factors may lead to inaccuracies.

Over a long period of time, it is found that the probability of a train from Bewford to London being late is 0.2 - OCR - GCSE Maths - Question 7 - 2021 - Paper 1

Worked Solution & Example Answer:Over a long period of time, it is found that the probability of a train from Bewford to London being late is 0.2 - OCR - GCSE Maths - Question 7 - 2021 - Paper 1

i) Complete the tree diagram.

ii) Work out the probability that both trains are not late.

iii) Give a reason why the probabilities used in the tree diagram for the second train may not be reliable.

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