A vaccine has 90% probability of being effective in preventing a certain disease. the probability of getting the disease if the
person is not vaccinated is 50%. in certain geographic region, 25% of the people get vaccinated. if a person is selected at random , find the probability that he or she will contract the disease
If 25% of the people <em>are</em> vaccinated, then 75% of the people are <em>not</em> vaccinated. Of those not vaccinated, each has a 50% chance of contracting the disease. The probability that someone is both not vaccinated and contracts the disease is (0.75)(0.5)=0.375. The probability that someone is vaccinated and contracts the disease is (0.25)(0.1)=0.025 (it is multiplied by 0.1 because if the vaccine is 90% effective, then there is a 10% chance someone that is vaccinated can contract the disease. Add these together for the total: 0.375+0.025=0.4 There is a 40% chance that someone chosen at random will contract the disease.
