In order for a vaccine to be effective, it should reduce a person’s chance of acquiring a disease. Consider a hypothetical vaccine for malaria—a tropical disease that kills between 1.5 and 2.7 million people every year. Suppose the vaccine is tested with 500 volunteers in a village who are malaria free at the beginning of the trial. Two hundred of the volunteers will get the experimental vaccine and the rest will not be vaccinated. Suppose that the chance of contracting malaria is 10% for those who are not vaccinated. Construct a two-way table to show the results of the experiment if:
(a) The vaccine has no effect.
(b) The vaccine cuts the risk of contracting malaria in half.