Question

EX. - An automobile association offers its members a towing service. For a monthly fee of $15 it will provide unlimited towing for free in case of a breakdown..Based on past data there is a 2 in 100 chance that a member will need one tow in a month; there is a 3 in 500 chance that a member will need two tows in a month, and no member ever needs more than 2 tows in a month. Suppose it costs the association $140 to provide one tow. Let Y = the association’s net monthly revenue (profit) from each member who enrols in the program.

a) Construct a probability distribution table of Y

Answer 1

The monthly charges are $15.

Probability that a member needs no tow in a month is in that case the profit is $15

Probability that a member needs one tow in a month is , and in that case the association has the profit is

Probability that a member needs two tow in a month is , and in that case the association has the profit is

Hence the distribution of Y is

Y	15
P(Y=y)