The foreclosure crisis has been particularly devastating in housing markets in much of the south and west United States,but even when analysis is restricted to relatively strong housing markets the numbers are staggering.For example,in 2011 an average of three residential properties were auctioned off each weekday in the city of Boston,up from an average of one per week in 2005.What is the probability that at least one foreclosure auction occurred in Boston on a randomly selected weekday of 2011?
A) 0.0498
B) 0.1494
C) 0.8009
D) 0.9502

Question

Quizplus · Accepted Answer

To find the probability of at least one foreclosure auction occurring on a randomly selected weekday of 2011, we need to find the complement probability of none of the auctions occurring.

The average number of residential properties auctioned off per weekday in 2011 = 3. 
The number of weekdays in 2011 = 365.

Therefore, the expected number of residential properties auctioned off in Boston in 2011 = 3 x 365 = 1095.

The probability of none of the auctions occurring on a randomly selected weekday = (1 - 1/1095)^365 = 0.0498 (rounded to four decimal places).

The probability of at least one auction occurring on a randomly selected weekday = 1 - 0.0498 = 0.9502 (rounded to four decimal places).

Therefore, the best answer is D, with a probability of 0.9502.

The Foreclosure Crisis Has Been Particularly Devastating in Housing Markets