SOLUTION: In a certain large city the proportion of people without a vehicle is twice that of those with one vehicle. The proportion with one vehicle is twice that of those with two vehicles
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Question 428028: In a certain large city the proportion of people without a vehicle is twice that of those with one vehicle. The proportion with one vehicle is twice that of those with two vehicles. The proportion with two vehicles is equal to that for those who own three or more vehicles. If a person is selected at random from that population, what is the probability that person will own exactly one vehicle?
I don't know how to wrap my head around this. Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website! let x = the proportion of people who own 3 or 4 vehicles.
this makes x = the proportion of people who own 2 vehicles.
this makes 2x = the proportion of people who own 1 vehicle.
this makes 4x = the proportion of people who own no vehicles.
the total population is made up of x + x + 2x + 4x = 8x.
person is selected at random from the population.
probability that the person will own exactly 1 vehicle is 2x / 8x = 1/4.
let's put this into numbers and see if it holds up.
assume 100 people own 3 or more vehicles.
you get 100 more people who own exactly 2 vehicles.
you get 200 more people who own exactly 1 vehicle.
you get 400 more people who own no vehicles.
total population is 800 people.
pick a person at random.
probability that the person owns exactly 1 vehicle is 200 / 800 = 1/4
