Question from http://sgforums.com/forums/2297/topics/345310
In a city, 20% of the citizens are carriers of a certain disease.If a citizen is a carrier, the probabbility that a blood test will indicate a positive result is 0.95. If citizen is a non-carrier, the probability that the blood test will indicate a postive result is 0.10. Two citizens are selected at random for the blood test. Find the probability that
(a) both citizens have positive results
(b) both citizens have negative results
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Answer:
(a) P(positive results) = 0.2 * 0.95 + 0.8 * 0.1 = 0.27
P(both citizens have positive results)
= P(positive results) * P(positive results)
= 0.27 * 0.27
= 0.0729
(b) P(negative results) = 0.2 * 0.05 + 0.8 * 0.9 = 0.73
P(both citizens have negative results)
= P(negative results) * P(negative results)
= 0.73 * 0.73
= 0.5329
