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 300 volunteers in a village who are malaria free at the beginning of the trial. One hundred of the volunteers will get the experimental vaccine and the rest will not be vaccinated. Suppose that the chance of contracting malaria is 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.

Step-by-step explanation:

Let assume that Suppose the chance of contracting malaria is 10% for those who are not vaccinated ;   (since the value) is not given.

Thus;

If the vaccine has no effect, risk of malaria for vaccine and no vaccine are equal to 0.1

Probability of not getting malaria if vaccinated or no vaccinated = 1 - 0.1 = 0.9

                          Malaria                No Malaria               Total

Vaccinated     100 * 0.1 = 10        100 * 0.9 = 90                         100

No Vaccine     200 * 0.1 = 20   200 * 0.9 = 180        300-100 = 200

Total                 20 + 10 = 30       90 + 180 = 270                       300

If the vaccine cuts the risk by half, risk of malaria for vaccinated are equal to 0.1/2 = 0.05

Probability of not getting malaria if vaccinated = 1 - 0.05 = 0.95

                          Malaria                No Malaria               Total

Vaccinated     100 * 0.05 = 5         100 * 0.95 = 95                 100

No Vaccine     200 * 0.1 = 20   200 * 0.9 = 180        300-100 = 200

Total                 20 + 5 = 25       90 + 180 = 275                         300