Question

GAG is considering giving every customer of one of their subsidiaries a free defensive driving course. The course teaches drivers to completely avoid: (1) side-swiping other vehicles (for which the company spends $4000 per accident) and (2) hitting fire-hydrants (for which the company spends $500 per accident). The following likelihoods have been previously determined: • There is a 1 in 100 chance that a driver will be involved in a side-swiping (1) accident. • There is a 1 in 10 chance that a driver will be involved in hitting a fire-hydrant (2).

Is offering this course worth it if the course costs GAG $100 per participant?

Answer 1

X : Amount GAG spends on accidents

course costs GAG $100 per participant

E(X) : Expected amount GAG spends on accidents per customer

Offering course is worth if Cost of course for GAG per customer < Expected amount GAG spends on accidents per customer

(1) side-swiping other vehicles (for which the company spends $4000 per accident) , There is a 1 in 100 chance that a driver will be involved in a side-swiping (1) accident

i,e

Accidents due Side-swiping , company spends $4000 per acident, Probability that a driver will be involed in a side-swiping (1) = P(X=4000) = 1/100

(2) hitting fire-hydrants (for which the company spends $500 per accident).here is a 1 in 10 chance that a driver will be involved in hitting a fire-hydrant (2)

i,e

Accidents due to hitting fire-hydrants , company spends $500 per acident, Probability that a driver will be involed in a hitting a fire-hydrant (2) = P(X=500) = 1/10

E(X) : Expected amount GAG spends on accidents per customer

As Cost of course for GAG per customer : 100 >  Expected amount GAG spends on accidents per customer: 90; Offering this course is not worth .