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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

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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:

  1. 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
  2. Therefore, the combined probability of not being late on either day: P(extnotlatebothdays)=0.85imes0.85=0.7225P( ext{not late both days}) = 0.85 imes 0.85 = 0.7225

  3. Now, we subtract this from 1 to find the probability of being late on at least one day: P(extlateatleastoneday)=1P(extnotlatebothdays)=10.7225=0.2775P( ext{late at least one day}) = 1 - P( ext{not late both days}) = 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.

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