Ataxia-telangiectasia (A-T) is a neurological disorder that weakens immune systems and causes premature aging. Science News reports that when both members of a couple carry the A-T gene, their children have a 1 in 5 chance of developing the disease.
a. Consider 15 couples in which both members of each couple carry the A-T gene. What is the probability that more than 8 of 15 couples have children that develop the neurological disorder?
b. Consider 10,000 couples in which both members of each couple carry the A-T gene. Is it likely that fewer than 3,000 will have children that develop the disease?