## Related questions with answers

Building permits were issued last year to three contractors starting up a new subdivision: Tara Construction built two houses; Westview, three houses; and Hearthstone, six houses. Tara’s houses have a 60% probability of developing leaky basements; homes built by Westview and Hearthstone have that same problem 50% of the time and 40% of the time, respectively. Yesterday, the Better Business Bureau received a complaint from one of the new homeowners that his basement is leaking. Who is most likely to have been the contractor?

Solution

VerifiedLet

$A_1$= Tara Construction

$A_2$= Westview

$A_3$= Hearthstone

$B$=Leaky basement

Given:

$P(B|A_1)=60\%=0.6$

$P(B|A_2)=50\%=0.5$

$P(B|A_3)=40\%=0.4$

Bayes's theorem:

$P(A_i|B)=\dfrac{P(B|A_i)P(A_i)}{\sum_{j=1}^k P(B|A_j)P(A_j)}$

## Create a free account to view solutions

## Create a free account to view solutions

## Recommended textbook solutions

#### An Introduction to Mathematical Statistics and Its Applications

6th Edition•ISBN: 9780134114217 (1 more)Morris L. Marx, Richard J. Larsen#### Probability and Statistics for Engineers and Scientists

9th Edition•ISBN: 9780321629111 (4 more)Keying E. Ye, Raymond H. Myers, Ronald E. Walpole, Sharon L. Myers#### The Practice of Statistics for the AP Exam

5th Edition•ISBN: 9781464108730Daniel S. Yates, Daren S. Starnes, David Moore, Josh Tabor#### Statistics and Probability with Applications

3rd Edition•ISBN: 9781464122163Daren S. Starnes, Josh Tabor## More related questions

1/4

1/7