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 Second train Late Late Not 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 Tree diagrams: 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

One morning there are two trains from Bewford to London.

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Answer

To complete the tree diagram, we need to identify the probabilities associated with the second train based on the information provided. Since the first train has a probability of 0.2 being late, it has a probability of 0.8 being not late. The probabilities for the second train should follow the same pattern unless stated otherwise. Thus:

For the second train:
- Late: 0.2
- Not late: 0.8

This gives us completed branches for the two trains where:

First train: Late (0.2), Not late (0.8)
Second train: Late (0.2), Not late (0.8)

Step 2

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 the probabilities of each train being not late:

Probability (First train not late) = 0.8
Probability (Second train not late) = 0.8

Thus, the combined probability is: $ext{P(Both not late)} = P( ext{First not late}) imes P( ext{Second not late}) = 0.8 imes 0.8 = 0.64$

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

Step 3

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 used in the tree diagram for the second train may not be reliable because they assume that the two trains operate independently of one another. External factors, such as weather conditions, scheduling conflicts, or delays from the first train, could affect the likelihood of the second train being late or not late. Therefore, the assumption of independence might not hold true in real-world scenarios.

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

One morning there are two trains from Bewford to London.

Work out the probability that both trains are not late.

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

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