Question

4. RATSA is planning to enforce speed limits along Great North road by
using speed cameras at 4 different locations, L1, L2, L3 and L4. The
speed camera at L1 is operated 50% of the time, the speed camera at
L2 is operated 30% of the time, the speed camera at L3 is operated 20%
of the time and the speed camera at L4 is operated 40% of the time.
A person who is speeding from for work has probabilities 0.2, 0.1, 0.5
and 0.2 respectively, of passing through these locations.
(i) What is the probability that the person will receive a speed ticket?
(ii) If the person received the speed ticket, what is the probability
that it was at L3 where he violated speed limit rules?

Answer 1

i) Person can receive a ticket by passing either through L1 camera or L2 or L3 or L4. Therefore:

P(receive a speed ticket) = $0.5\cdot0.2+0.3\cdot0.1+0.2\cdot0.5+0.4\cdot0.2=0.31$

ii) It is to determine the conditional probability:

P(receive a speed ticket given it was L3 camera) =

P = $\frac{0.5\cdot0.2}{0.5\cdot0.2+0.3\cdot0.1+0.2\cdot0.5+0.4\cdot0.2}=\frac{0.1}{0.31}=0.32$