In a car park, there are 100 vehicles, 85 of them being cars, 10 lorries and 5 buses. If they are all equally likely to leave, what is the probability of a car leaving second if a bus left first?
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P(x) represents the probability of an event x.
P(car leaving second/bus left first)= P(union of car leaving second and bus left first)/P(bus left first).
P(bus left first)= 5/100=1/20.
P(union of car leaving second and bus left first)= P(car leaving second).P(bus left first)= 85/99(1/20)=17/396.So
P(car leaving second/bus left first)=17/396/(1/20)=
17×20/396=340/396=85/99.
P(car leaving second/bus left first)= P(union of car leaving second and bus left first)/P(bus left first).
P(bus left first)= 5/100=1/20.
P(union of car leaving second and bus left first)= P(car leaving second).P(bus left first)= 85/99(1/20)=17/396.So
P(car leaving second/bus left first)=17/396/(1/20)=
17×20/396=340/396=85/99.
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