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Date November 2015 Marks available 6 Reference code 15N.2.hl.TZ0.6
Level HL only Paper 2 Time zone TZ0
Command term Find Question number 6 Adapted from N/A

Question

Josie has three ways of getting to school. 30% of the time she travels by car, 20% of the time she rides her bicycle and 50% of the time she walks.

When travelling by car, Josie is late 5% of the time. When riding her bicycle she is late 10% of the time. When walking she is late 25% of the time. Given that she was on time, find the probability that she rides her bicycle.

Markscheme

EITHER

     M1A1A1

 

Note:     Award M1 for a two-level tree diagram, A1 for correct first level probabilities, and A1 for correct second level probabilities.

 

OR

P(B|L)=P(L|B)P(B)P(L|B)P(B)+P(L|C)P(C)+P(L|W)P(Q)(=P(BLP(L))     (M1)(A1)(A1)

THEN

P(B|L)=0.9×0.20.9×0.2+0.95×0.3+0.75×0.5(=0.180.84)     M1A1

=0.214(=314)     A1

[6 marks]

Examiners report

[N/A]

Syllabus sections

Topic 5 - Core: Statistics and probability » 5.4 » Use of Bayes’ theorem for a maximum of three events.

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