Question

According to the Mortgage Bankers Association, 11% of US mortgages were delinquent in Texas in the second quarter of last year. A delinquent mortgage is one that has missed at least one payment but has not yet gone to foreclosure. A random sample of six mortgages in Texas was selected. What is the probability that one or more of these mortgages is delinquent? A.0.1737 B. 0.2236 C.0.5632 D. 0.5030

Answer 1

To find the probability that one or more of the mortgages is delinquent, we can use the complement rule and subtract the probability that none of the mortgages are delinquent from 1.

Step-by-step explanation:

To solve this problem, we can use the complement rule. The probability that none of the mortgages are delinquent is equal to 1 minus the probability that one or more mortgages are delinquent. From the given information, we know that 11% of mortgages are delinquent in Texas. Therefore, the probability that a single randomly selected mortgage is delinquent is 0.11.

To find the probability that none of the mortgages are delinquent, we raise this probability to the power of the number of mortgages in the sample, which in this case is 6. So the probability that none of the mortgages are delinquent is (1 - 0.11)^6 = 0.405.

Finally, we can calculate the probability that one or more mortgages are delinquent by subtracting the probability that none of the mortgages are delinquent from 1. So the probability that one or more mortgages are delinquent is 1 - 0.405 = 0.595.

Therefore, the correct answer is D. 0.595.