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 0.2 Not late 0.8 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 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

One morning there are two trains from Bewford to London.

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Answer

To complete the tree diagram for the second train, we need to assume the same probabilities for the second train as the first train since no other information is provided. Therefore, the second train can also be defined as:

            Late                     0.2

            Not late                0.8

So the complete tree diagram will look like this:

First train             Second train
Late                     Late                   0.2 * 0.2 = 0.04
                Not late                0.2 * 0.8 = 0.16

Not late                Late                   0.8 * 0.2 = 0.16
                Not late                0.8 * 0.8 = 0.64

Step 2

Work out the probability that both trains are not late.

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Answer

The probability that both trains are not late is given by:

$P(Not late) = P(Not late ext{ first train}) imes P(Not late ext{ second train})$

Hence,

$P(Not late) = 0.8 imes 0.8 = 0.64$

Thus, 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 for the second train may not be reliable because they are based on historical data from the first train. Factors such as different time slots, weather conditions, or operational changes could significantly affect the punctuality of the second train, leading to different probabilities than those assumed.

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

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

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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