1a. A large artificial insemination stud has just purchased a promising Red Angus bull. Management is concerned, however, that the bull might be a carrier of osteopetrosis (marble bone disease), a recessive lethal condition. Assume that there is no DNA test for the recessive allele. Five percent of all cows are thought to be carriers of the osteopetrosis allele. A.I. matings to randomly selected cows have already produced 87 normal calves and no osteopetrosis calves. What is management's level of confidence that the bull is not a carrier of the osteopetrosis allele? (Remember - "confidence" is the probability of detection if the animal being tested is a carrier of the recessive allele.)
1b. Given the information in question 1a, how many A.I. matings to randomly selected cows, with each mating resulting in 1 calf, are required to be 95% confident that the bull does not carry the osteopetrosis allele?
1c. If the bull in question 1a sires a calf with osteopetrosis next year, what will be management's level of confidence that the bull carries the osteopetrosis allele?
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