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

Let

B : event that  the household have vehicles in Boston, Massachusetts.

C : event that  the household have vehicles in Cambridge, Massachusetts.

W: event that  the household have vehicles in Worceter, Massachusetts.

Given,

P(B) =66.2 % = 0.662

P(B) =63.2% = 0.632

P(C) = 80.7% = 0.807

Since, owning a vehicle in these three cities are independent of each other. Hence we can use multiplicative law of probability to find,

The probability that all three households has a vehicle, if a household from each city is randomly select

= P(B)* P(C) * P(W)

=0.662 * 0.632 * 0.807

=0.3366