Question

"According to a study, the percentage of households with vehicles in Boston, Massachusetts, is 66.2%; in Cambridge, Massachusetts, 63.2%; and in Worceter, Massachusetts, 80.7%. Suppose owning a vehicle in these three cities are independent of each other. If a household from each city is randomly selected, What is the probability that all three households has a vehicle."

Answer 1

The probability that all three households will have a vehicle is 0.338 or 33.8%

Explanation:

Percentage of households with vehicles is Boston = 66.2%

This means, if a household is randomly chosen in Boston, the probability that it will be a vehicle = 66.2% = 0.662

Percentage of households with vehicles is Cambridge = 63.2%

This means, if a household is randomly chosen in Cambridge, the probability that it will be a vehicle = 63.2% = 0.632

Percentage of households with vehicles is Worceter = 80.7%

This means, if a household is randomly chosen in Worceter, the probability that it will be a vehicle = 80.7% = 0.807

It has been given that owning a vehicle in these cities is independent of each other. According to the fundamental rule of probability, the joint probability of two or more independent events is equal to the product of their individual probabilities.

So, if a household is chosen from each these cities, the probability that all three will have a vehicle will be:

0.662 x 0.632 x 0.807 = 0.338 = 33.8%

Thus, the probability that all three households will have a vehicle is 0.338 or 33.8%