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

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Mathematics

Henry Shaw

3 March, 08:54

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

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Kyler Shepherd · Answer 1

If 25% of the people are vaccinated, then 75% of the people are not 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.