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(B∩L′P(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]