AQA S1 2010 January — Question 4

Exam BoardAQA
ModuleS1 (Statistics 1)
Year2010
SessionJanuary
TopicProbability Definitions
TypeMultiple independent trials

4 Each school-day morning, three students, Rita, Said and Ting, travel independently from their homes to the same school by one of three methods: walk, cycle or bus. The table shows the probabilities of their independent daily choices.
\cline { 2 - 4 } \multicolumn{1}{c|}{}WalkCycleBus
Rita0.650.100.25
Said0.400.450.15
Ting0.250.550.20
  1. Calculate the probability that, on any given school-day morning:
    1. all 3 students walk to school;
    2. only Rita travels by bus to school;
    3. at least 2 of the 3 students cycle to school.
  2. Ursula, a friend of Rita, never travels to school by bus. The probability that: Ursula walks to school when Rita walks to school is 0.9 ; Ursula cycles to school when Rita cycles to school is 0.7 . Calculate the probability that, on any given school-day morning, Rita and Ursula travel to school by:
    1. the same method;
    2. different methods.