Instructions For each question, your answer must be based on an analysis of cond
ID: 3142215 • Letter: I
Question
Instructions For each question, your answer must be based on an analysis of conditional probability and/or independence. You must state each event relevant to the problem under consideration, and the formulas you use. Just writing down an answer or calculation without basing it on the relevant formula(s) on probability and conditinoal probability will earn zero credit (even if the answer is correct).
I am thinking of buying a used vehicle. I can choose from one of three types: a hatchback, a sedan, or an SUV. There are 9 hatchbacks I am considering, of which 3 have antilock brakes. There are 10 sedans I am considering, of which 6 have antilock brakes. There are 6 SUVs I am considering, of which 3 have antilock brakes.
(a) If I choose at random from all of the vehicles I am considering, what is the probability that the vehicle I choose will be an SUV with antilock brakes?
(b) If I first choose a type of vehicle at random and then choose a vehicle of that type at random, what is the probability that the vehicle I choose will be an SUV with antilock brakes?
Explanation / Answer
(a) Total number of hatchbacks = 9
Number of hatchbacks with antilock brakes = 3
Total number of sedans = 10
Number of sedans with antilock brakes = 6
Total number of SUVs = 6
Number of SUVs with antilock brakes = 3
Probability that an SUV has antilock brakes = 3/6 = 1/2
Total number of vehicles = 9 + 10 + 6 = 25
Probability that an SUV is chosen = 6/25
Thus the probability that the vehicle chosen is an SUV with antilock brakes = 6/25 * 1/2 = 3/25 = 0.12
(b) Total number of hatchbacks = 9
Number of hatchbacks with antilock brakes = 3
Total number of sedans = 10
Number of sedans with antilock brakes = 6
Total number of SUVs = 6
Number of SUVs with antilock brakes = 3
Probability that an SUV has antilock brakes = 3/6 = 1/2
Total number of vehicles = 9 + 10 + 6 = 25
Probability that the type chosen is an SUV = 1/3
Thus the probability that the vehicle chosen is an SUV with antilock brakes = 1/3 * 1/2 = 1/6 = 0.17