Answer to Question #144682 in Statistics and Probability for Kyra Viray

Question

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 enrolls in the program.
Provide a probability distribution table for Y

Answer 1

P(1)=2/100=0.02

P(2)=3/500=0.006

P(0)=1-0.02-0.006=0.974

Profit for P(1)=[Fee]-[Costs for 1 tow]=15-140=-125

Profit for P(2)=[Fee]-[Costs for 2 tow]=15-280=-265

Profit for P(0)=[Fee]=15

probability distribution table

Number of tows Probability Profit

0 0.974 15

1 0.02 -125

2 0.006 -265