The National Association of Realtors released a survey indicating that a surprising 43% of first-time home buyers purchased their homes with no-money-down loans during 2005. The fear is that house prices will decline and leave homeowners owing more than their homes are worth. PMI Mortgage Insurance estimated that there existed a 50% risk that prices would decline within two years in major metro areas such as San Diego, Boston, Long Island, New York City, Los Angeles, and San Francisco. A survey taken by realtors in the San Francisco area found that 12 out of the 20 first-time home buyers sampled purchased their home with no-money-down loans. Calculate the probability that at least 12 in a sample of 20 first-time buyers would take out no-money-down loans if San Francisco's proportion is the same as the nationwide proportion of no-money-down loans.
a. 0.0441
b. 0.0124
c. 0.0512
d. 0.0618