SOLUTION: 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 p

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(52788) (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.
~~~~~~~~~~~~~~~~~~~~~

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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