Mary travels to work by train every day:
The probability that her train will be late on any day is 0.15 - Edexcel - GCSE Maths - Question 11 - 2019 - Paper 2
Question 11
Mary travels to work by train every day:
The probability that her train will be late on any day is 0.15.
(a) Complete the probability tree diagram for Thursday and ... show full transcript
Worked Solution & Example Answer:Mary travels to work by train every day:
The probability that her train will be late on any day is 0.15 - Edexcel - GCSE Maths - Question 11 - 2019 - Paper 2
Step 1
Complete the probability tree diagram for Thursday and Friday.
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Answer
To complete the probability tree diagram:
For Thursday:
Probability of being late: 0.15
Probability of not being late: 1 - 0.15 = 0.85
For Friday:
The probabilities mirror Thursday's outcomes:
Probability of being late: 0.15
Probability of not being late: 0.85
The completed tree diagram will therefore show the two days with the following probabilities:
Thursday: Late (0.15), Not Late (0.85)
Friday: Late (0.15), Not Late (0.85)
Step 2
Work out the probability that her train will be late on at least one of these two days.
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Answer
To find the probability that her train will be late on at least one of the two days, we can use the complementary probability:
First, calculate the probability that her train is not late on both days:
Probability of not being late on Thursday: 0.85
Probability of not being late on Friday: 0.85
Therefore, the combined probability of not being late on either day:
P(extnotlatebothdays)=0.85imes0.85=0.7225
Now, we subtract this from 1 to find the probability of being late on at least one day:
P(extlateatleastoneday)=1−P(extnotlatebothdays)=1−0.7225=0.2775
Thus, the probability that her train will be late on at least one of these two days is 0.2775.