Question 1194470: Please assist me in solving this question below
A vaccine has a 90% probability of being effective in preventing a certain
disease. The probability of getting the disease if a
person is not vaccinated is 50%. In a 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.
Answer by ikleyn(52787)   (Show Source):
You can put this solution on YOUR website! .
Please assist me in solving this question below
A vaccine has a 90% probability of being effective in preventing a certain
disease. The probability of getting the disease if a
person is not vaccinated is 50%. In a 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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If a person is selected at random, then EITHER
(a) the probability that he or she was not vaccinated is 75%,
and then the probability for such a person to get a disease is 50%;
OR
(b) the probability that he or she was vaccinated is 25%,
and then the probability for such a person to get a disease is 100%-90% = 10%.
Taking it into account, the probability that a person selected at random
will contract the disease is
P = 0.75*0.5 + 0.25*0.1 = 0.4. ANSWER
Solved.
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