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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 20 - 2021 - Paper 1
Question 20
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 20 - 2021 - Paper 1
Step 1
Work out the probability that both trains are not late.
Answer
To find the probability that both trains are not late, we first need the probability for each train.
From the tree diagram, the probabilities for the first train being not late is:
- First Train: Not Late = 0.8
- Second Train: Not Late = 0.8 (assuming the same probability as the first train since no other information is provided).
The combined probability that both trains are not late can be calculated as:
Therefore, the probability that both trains are not late is 0.64.
Step 2
Give a reason why the probabilities used in the tree diagram for the second train may not be reliable.
Answer
The probabilities used in the tree diagram for the second train may not be reliable because they are based on historical data that might not represent current conditions. Factors such as increased train frequency, changes in scheduling, or external events like construction or severe weather can affect train punctuality. Hence, the earlier probabilities may not accurately reflect the current reliability of the service.