Homeowners Who Recently Bought Their Houses from a Local Developer

Multiple Choice

Homeowners who recently bought their houses from a local developer allege that 30% of the houses this developer constructs have some major defect that will require substantial repairs.To test this allegation, we randomly sample 20 houses constructed by the developer and find that two of the homes do, indeed, have some major defect.If the allegation is correct, what is the probability of observing at most two defective homes out of a random sample of 20?

A) 0.0256
B) 0.1000
C) 0.0300
D) 0.9744