Answer the following questions:

1 – Consider a breast cancer screening test with a sensitivity of 95%, and a specificity of 95% applied to a sample of 10,000 subjects. As of 2005, there were an estimated 2.521 million cases of breast cancer in the US population of approximately 295.560 million. Calculate

(a) The expected number of false positives in the given sample.

(b) The expected number of false negatives in the given sample.

(c) The PPV

(d) The NPV

(e) The accuracy of the test

2 - A dominantly inherited genetic disease is identified over several generations of a large family. However, about half of families have dominant disease with complete penetrance, whereby if a parent is affected, there is a 50% probability that any one offspring will be affected. Similarly, about half of families have dominant disease with reduced penetrance, whereby if a parent is affected; there is a 25% probability that any one offspring is affected. Suppose in a particular family one parent and two out of two offspring are affected. What s the probability that exactly two out of two offspring will be affected in a family with dominant disease with complete penetrance?

3 - What is the probability that exactly two out of two offspring will be affected in a family with dominant disease with reduced penetrance?

4 - What is the probability that the mode of transmission for this particular family is dominant with complete prenetrance? Is this a prior or a posterior probability?

**Subject Mathematics General Statistics**