Question

Students travel to school by shuttle, train, or car. 45% of all students arrive by shuttle, 35% by train and the rest by car. 20% of these students arriving by shuttle are late to school and 40% of the students arriving by train are late. If 35% of all students are late:

a) Find the probability that a student who arrives by car is late?

b) Find the probability that a student who was not late did not arrive by shuttle?

Answer 1

Let the event of the student being late be represented by L.

Let the events of the student arriving by shuttle be represented by S, by train as T and by car as C

Then,

P(S) = 0.45

P(T) = 0.35

P(C) = 0.20

P(L/S) = 0.20

P(L/T) = 0.40

P(L) = 0.35

a) We need to find P(L/C)

We know

b)

P(S'/ L') = P(C/L') + P(S/L')

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