A vaccine, which is currently in use, is known to be 80% effective. A pharmaceutical company has developed a newvaccine and the company claims that 90% of the people given the new vaccine will develop the immunity. Supposethe claim of the company is true, and the newly developed vaccine is given to 20 people. The expected number of people in the sample that will develop the immunity is: a) 90% b) 18% c) 16% d) 80%

The correct answer is B) 18%

Step-by-step explanation:

Note that the vaccine is already and is 80% effective. This means that if the entire population was administered with the vaccine, only 8/10 would gain immunity leaving 2/10 or 0.2 exposed.

If the new vaccine, therefore, is supposed to be 90% effective, it is only pragmatic to administer it against those who do not have immunity which is 0.2 of the existing population.

So to get the percentage that will develop immunity, we have:

0.2 x 0.9 = 0.18 or 18%

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